
716 F.Supp. 812 (1989)
Ann McLAUGHLIN, Secretary of Labor, U.S. Department of Labor, Plaintiff,
v.
DIALAMERICA MARKETING, INC., Defendant.
Civ. A. No. 81-4020.
United States District Court, D. New Jersey.
March 23, 1989.
*813 George Salem, Patricia Rodenhausen, Diane Z. Wade, and Louis De Bernardo, Evan Reid Barouch, U.S. Dept. of Labor, New York City, for plaintiff.
Mark R. Kook, Charles I. Poret, Sharfman, Shanman, Poret & Siviglia, New York City, and Bernard Dorfman, Hackensack, N.J., for defendant.
WOLIN, District Judge.
Currently pending before the Court is an action commenced by the Secretary of the United States Department of Labor ("Secretary") alleging that defendant DialAmerica Marketing, Inc. ("DialAmerica") violated the minimum wage and recordkeeping provisions of the Fair Labor Standards Act of 1938, 29 U.S.C. § 201 et seq. ("FLSA") in connection with its home telephone search program. Because of pronounced violations of the FLSA and a failure to pay a minimum wage to the participants in such program, the Court will order the payment of back wages and restrain DialAmerica from further withholding of minimum wages.

I. BACKGROUND
DialAmerica Marketing, Inc. is a Delaware corporation with offices in 20 states, including New Jersey, that employs over 2,400 people nationwide. For purposes of this action, DialAmerica concedes it is an enterprise within the meaning of Section 3(r) of the FLSA. Further, it agrees that it has gross volume of sales made or business done of not less than $250,000.00 and employees who are engaged in interstate commerce. Its business is telephone marketing of which a major part is the sale of magazine renewal subscriptions, its "expire" program. In order to sell these subscriptions, DialAmerica receives from publishers the name and address of subscribers whose subscriptions have or are about to expire. DialAmerica prints cards with the name and address of each subscriber ("expire cards"), has its employees attempt to locate a telephone number for each card, and then forwards the subscriber information to its sales offices throughout the country where telephone salespersons contact the subscribers in an attempt to sell magazines.
Initially, DialAmerica employed in-house researchers at its Teaneck, New Jersey location to obtain subscribers' telephone numbers from telephone books and from directory assistance. In 1976, DialAmerica expanded its telephone number search capacity by instituting a home researcher program. DialAmerica initially recruited home researchers through five advertisements in a local shopper newspaper, but after May 1979, all prospective home researchers, upon hearing about the program from friends or family members, sought out DialAmerica for the opportunity to do home research. These people made an appointment to speak to someone in DialAmerica's lead processing department. At that time they were taught how to fill out a magazine expire card, and those who desired the homework signed an independent contractor agreement. DialAmerica never rejected anyone who wanted to be a home researcher. Between 1980 and mid-1982, DialAmerica employed hundreds of home researchers.
The modus operandi employed by DialAmerica required that a home researcher travel to DialAmerica's Teaneck office. At that time he or she would be given a box of 500 cards to research and would make an appointment, generally for one week later, to return the cards and pick up new ones. If the researcher desired more time, he or she could reschedule the appointment. A home researcher could ask for as many cards as he or she wanted to research subject to a 500-card minimum and card availability. Experienced researchers would pick up as many as 3,000-4,000 cards per week. Researchers were restricted to the extent that they could not pick up a new group of cards to research until they had completed the group previously taken. The cards, when given to a home researcher, were presorted by state and area code, and home researchers were permitted to *814 request cards containing addresses from states of their choice.
These home workers then brought the cards home and attempted to obtain telephone numbers for the subscribers designated on each card. Numbers found were written on the card and the card became completed and compensable. The home researcher was unrestrained in the time he or she wanted to expend to complete the cards, since DialAmerica did not require a minimum or maximum number of hours. Nor was there an obligation to complete the cards that were taken. Some home researchers chose to spread the work over a full week regardless of the number of cards to research; some necessarily worked a full week because of the large number of cards; and some completed the work in two or three days. Each home researcher tailored his or her home research to fit his or her individual needs and life styles.
The home researchers were paid on a piece rate basis  initially five cents, later seven and then ten cents  for each subscriber telephone number found. Occasionally, the piece rate was higher for groups of cards which involved subscribers for whom numbers were difficult to locate (e.g., children) and where the success rates were particularly low. By contrast, in-house researchers were paid the FLSA minimum wage for all hours worked. DialAmerica also required the home researchers, unlike the in-house researchers, to fill out independent contractor or subcontractor applications and to sign independent contractor agreements.
In addition to the home researchers who picked up their cards directly from DialAmerica's Teaneck office, six or seven home researchers ("distributors") also distributed cards to other home researchers ("distributees") who could or would not travel to the Teaneck office. The distributors received one cent above the piece rate for each number found by their distributees. They received one check for the gross amount of all listed numbers found by them and by the distributees to whom they gave cards. Some of the distributors paid their distributees the full piece rate and kept the one cent; others paid less than the piece rate to their distributees. Originally, DialAmerica required the distributors to obtain signed independent contractor's agreements from their distributees. Copies of these agreements were initially retained by DialAmerica. Later in the program, when it ceased to require distributees to sign such agreements, the existing agreements were discarded. These distributors were not subject to any supervision from DialAmerica in running their distributor operations. DialAmerica had no contact with the distributees and does not possess records of the names of the distributees.
For each of the home researchers (other than for distributees), DialAmerica maintained detailed records listing for each week the number of cards the home researcher received, the applicable piece rate, the number of cards for which listed telephone numbers were found and the total amount paid for that week. Because DialAmerica erroneously believed that the home researchers were not "employees" and were properly paid at a piece rate, DialAmerica did not keep any records of the number of hours the home researchers worked or the number of cards any of them could research in an hour (i.e., their respective production rates). Nor did DialAmerica require the home researchers to maintain a handbook recording the number of hours they worked. Thus, no home researcher kept any record of the rate per hour at which he or she could research cards.
In June 1982, during the pendency of this lawsuit, DialAmerica ceased the home research program and terminated the employment of all of the home researchers except for a few who commenced working at defendant's Teaneck office.

II. PROCEDURAL HISTORY
This case was initiated by the Secretary of the Department of Labor alleging that defendant DialAmerica willfully violated the minimum wage and recordkeeping provisions *815 of FLSA in connection with its home telephone research program.
By an Opinion and Order dated January 26, 1984, this Court (Stern, J.) dismissed the complaint and awarded summary judgment to DialAmerica on the ground that the home researchers and distributors were not "employees" within the meaning of FLSA § 203, but were instead independent contractors. The Third Circuit Court of Appeals affirmed that decision in part and reversed in part on March 13, 1985, finding that the distributors were independent contractors, but that home researchers were statutory employees. Donovan v. DialAmerica, 757 F.2d 1376 (3d Cir.), cert. denied, 474 U.S. 919, 106 S.Ct. 246, 88 L.Ed.2d 255 (1985). The Third Circuit remanded the matter to this Court for a hearing on the Department's claim that DialAmerica had not satisfied the minimum wage and recordkeeping provisions of the FLSA with respect to the home researchers.
On October 27, 1987 this Court (Lechner, J.) granted DialAmerica's motion for partial summary judgment, holding that DialAmerica did not willfully violate the FLSA in treating home researchers as non-employees to whom the FLSA did not apply. The Court held that DialAmerica was not aware that its classification of home researchers as independent contractors was in violation of the FLSA and that its actions were not in "reckless disregard of the FLSA" pursuant to the Third Circuit standard set forth in Brock v. Richland Shoe, 799 F.2d 80, 81 (3d Cir.1986), aff'd, 486 U.S. 128, 108 S.Ct. 1677, 100 L.Ed.2d 115 (1988). The Court also held that the Department's failure to reveal any evidence indicating willful behavior on the part of DialAmerica warranted the application of the standard two-year statute of limitations under the FLSA (as opposed to the three-year limitations period applicable to willful violations).[1]
A bench trial was held on September 6, 7, 8, 22 and 23, 1988 in which this Court considered whether the Department could sustain its burden of proving that DialAmerica failed to comply with the minimum wage provisions of the FLSA with regard to any individual home researcher, and if so, whether the Court may order the payment of back wages to such persons. Necessary to that decision is the determination, through either direct or representative testimony, of the number of hours worked by each home researcher.

III. EVIDENCE PRODUCED AT TRIAL

A. Former Home Researchers  Raw Data

The bulk of the evidence presented at trial consisted of the testimony of 43 former home researchers, 24 live before the Court and 19 by deposition. With respect to each witness, the identical inquiries were made, namely, the number of cards completed per week; the number of hours expended per day and per week to complete a given number of cards; the method by which each witness engaged in the researching process; the usual number of telephone listings each could receive from an operator; the amount of money received per card researched; and finally, an estimate of the number of cards per hour that could be completed by the witness. Most witnesses received between 500 and 1,500 cards per week and processed them at rates on the average falling between 30 and 60 cards per hour. The witnesses generally testified to their ability to obtain between two and three listings from one operator, but claimed that some states were more generous in providing multiple listings.
Initially, home researchers were paid five cents per number found. That amount subsequently increased to seven and then to 10 or 20 cents per number found. In 1980, the FLSA minimum wage was $3.10/hour, increasing to $3.35/hour in *816 1981 and 1982.[2] Most home researchers also testified that they were provided with written instructions directing them to pass over cards naming all schools, libraries, army bases, government installations and hospitals.[3]
The witnesses at trial were asked whether they kept records of the hours spent researching a given number of cards. Several replied that they had maintained records at one time, but have since disposed of them; several claimed that they had timed themselves, but had never recorded their hours; and several, namely, Christine Poss, Thomas Milo, Rina Herdman and Roxanne Catrambone, submitted their records to the Court.[4]
Those former home researchers who submitted records also operated as distributors, and their records set forth the number of cards given to distributees; the number of listed numbers found by the distributees; the amount paid by the distributor to the distributee; and in some cases, the rate of pay (i.e., five cents/card), including the commission received by the distributor at one cent above the rate received by the distributee. However, the number of hours worked by each employee was not recorded and was unavailable to the Court.
Despite these somewhat detailed records, the principal issue persists: What was the production rate of each home researcher? This inquiry is necessarily relevant to the crucial determination of back wages due, and cannot be answered until the number of hours worked by each home researcher is ascertained. Since none of the testifying witnesses recorded the number of hours worked, this Court must, among other factors, look to their recollective estimates.

B. Compliance Specialist  Statistical Data


(1) Calculation of Hours Worked
In an effort to resolve the issue as to rates of production, the Department of Labor called compliance specialist William Devins as an expert witness. Devins testified that he was assigned the task of developing a computerized summary of all of the available data, including both the business records of DialAmerica[5] and the records supplied by several former home researchers.
Because all available data were incomplete, Devins developed and advanced a number of mathematical formulae designed to solve for particular variables depending upon the information provided by the records under consideration.
First, he assumed that a worker who is able to process 50 cards/hour (a figure readily ascertained from individual witness testimony) would expend 10 hours to complete 500 cards in one week.[6]
           500 received = 10 hours
           ____________
             50/hour
In order to earn the minimum wage in that particular week, the worker would have had to be paid $31.00. ($3.10 × 10 hours)[7]

(2) Calculation of Cards/Hour
Devins' formula to solve for an unknown number of cards/hour is
 cards/hour = minimum wage × cards processed[8]
             ________________________________
                   minimum wage due
The production rate for the hypothetical employee would, therefore, equal
         $3.10 × 500 = 50 cards/hour
         ____________
            $31.00
Hence, if the minimum wage due ($31.00 with our hypothetical researcher) is equal *817 to actual pay, then the calculation of cards/hour will reveal the number of cards that this worker would have had to process in the week in question in order to earn the minimum wage.

(3) Calculation of Number of Cards/Hour Below Which a Minimum Wage Violation Exists
Assuming that the following information is available for the hypothetical employee,


          Min.                       Actual
  Date    Wage   Rec'd.  Lstd. Rate   Pay
1/20/80   $3.10  1359    416   0.20  $83.20

the inquiry here is what number of cards/hour would this worker have had to process in order for actual pay received ($83.20) from DialAmerica to have sufficiently provided the minimum wage of $3.10 in 1980?[9] Devins suggests that the proper formula is
  cards/hour = minimum wage × cards processed
             ______________________________
                      gross pay
Inserting the known sample data,
     cards/hour = $3.10 × 1359 = 51.
                  _____________
                     $83.20
This solution demonstrates that this employee would have had to process 51 cards/hour in order for $83.20 to provide the appropriate minimum wage.[10] With a production rate of 50 cards/hour, this employee would be one card short of the number necessary in order for her actual pay to provide the minimum wage.
Appendix A further displays Devins' mathematical analysis by providing a sample work week for each testifying employee (excluding distributees), and indicating the rate of production (i.e., cards/hour) that each worker would have had to achieve in the given week in order for actual salary received to reach the equivalent of the minimum wage.
Clearly, only three of the 33 witnesses accounted for in Appendix A achieved, or conceivably could have achieved, the rates of production required to render their given salaries consistent with the appropriate minimum wage.[11] As for the remaining thirty witnesses, the numbers in the far righthand column ("Minimum Wage Viol. Below Indicated Cds/Hr.") establish obvious violations in the sample weeks. For instance, M. Sullivan, in receipt of 545 cards, would have had to, based upon Devins' formula, process cards at the impossible rate of 98/hour in order for her actual pay to provide the minimum wage. However, most employees testified to rates falling only between 30 and 60 cards/hour.
A pattern of violations with regard to those not testifying can be inferred based on the representative testimony of these witnesses. Appendix B demonstrates similar unattainable rates of production for a sampling of 20 non-testifying employees. In fact, only two non-testifying witnesses in this random sample could have achieved the rate of production required to render her actual pay equal to the minimum wage (F. Hecht, at 45 cards/hour and M. Paolacci, at 25 cards/hour).

(4) Calculation of Back Wages Due
Continuing with the prior hypothetical home researcher, the next variable to be determined is the amount of back wages due. Once again, with an assumed rate of 50 cards/hour, Devins reasons that
Back wages due = (cards received × minimum wage) - actual pay
                 _______________
                   cards/hour
               = 1359 × $3.10 - $83.20
                 ____
                  50
               = 27.18 × $3.10 - $83.20
               = $84.26 - $83.20 = $1.06
*818 Therefore, the hypothetical employee should have received $84.26 at the minimum wage. Since the actual pay was only $83.20, a minimum wage violation of $1.06 occurred. Devins excluded this figure ("wage violation") from his computerized summary due to the missing data concerning the number of hours worked by each employee. He testified that once a number of cards per hour is determined for an employee or a group of employees, that number would then be inserted into the computer in the cards/hour slot for a calculation of the back wages due in each work week.[12]

(5) Calculation of Cards Received
Another variable that confronted the Department of Labor was the determination of the total number of cards received when the only information available was the number of listed cards (i.e., telephone numbers found) and the rate paid for these listed cards. To make this determination, Devins used data concerning the "find rates" for various rates of pay per card. For instance, 50-cent cards were found at a rate of 17.43%, 5-cent cards were found at a rate of 57.67%, and 10-cent cards were found at a rate of 37.18%. Armed with this data, Devins postulated that the number of cards received by a given researcher was algebraically ascertainable. Thus, he proposed the following formula[13]:
              100%   =   ×
           _________   _______
           find rate   listed
For the hypothetical researcher:
  100%  =   ×
 ______  ______
 37.18%  listed
  100%  =  ×
 ______   ____
 37.18%   416
   × =   100%  × 416
       ______
       37.18%
   = 2.6 × 416 = 1119
Therefore, the hypothetical researcher who has found listings for 416 cards payable at the 10-cent rate would have received 1119 cards.

(6) Milo's Records
To further complicate matters, in the case of a distributorship, the number of cards allotted to the distributor and his or her distributees may be the unknown. The records of distributor Thomas Milo, for instance, set forth the total number of cards received from DialAmerica and the amount paid to each of his distributees, but the number of cards worked on by each distributee is unknown. To solve for the number of cards received by each distributee as well as by the distributor, Devins proposes
           distributor's gross =      ×
           ___________________   ___________
              total gross        cards rec'd
For example, if Milo received a total of 1000 cards from DialAmerica, paid $12.45 to one distributee and $10.40 to himself, and the total gross pay was $23.35, then the formula would apply as follows:
   10.40   =   ×
   _____    ____
   23.35    1000
   × = 10.40 × 1000
       _____
       23.35
           = .445 × 1000 = 445
The formula establishes that Milo received 445 cards out of the total 1000.
It once again becomes necessary to solve for the rate of cards per hour at which the minimum wage would be due to determine if a wage violation occurred. Devin proposes:
     cards/hour = minimum wage × cards rec'd
                  ___________________________
                      minimum wage due
                = 3.10 × 445    = 133
                  _______
                   10.40
Milo would, therefore, have to process cards at a rate of 133/hour for his salary *819 of $10.40 to reach the equivalent of minimum wage in the week in question.[14]

(7) Poss' Records  Calculation of Rate of Pay Per Card
In the case of the records maintained by distributor Christine Poss, Devins found that the rate of pay per card was not recorded. With actual pay received and the number of cards completed, actual pay must be divided by the number of cards completed to solve for the rate per card, that is:[15]
     rate per card =         actual pay
                     __________________________
                      number of cards completed
Therefore, in a week in which a distributee is paid $54.90 for the completion of 366 cards,
         rate per card = 54.90 = $0.15
                         _____
                          366
Here, in this example, the distributee was processing cards payable at the 15-cent rate.

(8) Poss' Records  Number of Cards Received by Distributees
Several of the records maintained by Poss indicate the rate of pay and exclude the number of cards received by a given distributee. To solve for cards received, the formula suggested is
          cards received = listed cards
                           ____________
                             find rate
Therefore, if a distributee working on cards payable at a rate of 8 cents (as indicated by the records of Poss) found 195 numbers (i.e., "listed" cards), and the find rate for 8-cent cards is 39.35%, then
         cards received = 195 = 495
                         _____
                         .3935
this employee would have received 495 cards.
A persistent and nagging question arose concerning the definition of a card "processed." It is the Department's position that the task of "processing" cards takes into account not simply time spent on the telephone, but includes the performance of whatever incidental tasks are necessary, such as unpacking and sorting cards by state.[16] Furthermore, Devins stated that a home researcher, in calculating the number of cards per hour that he or she is able to complete, would include cards passed over because the task of "processing" involves removing the cards from a package, and the determination that certain ones should not be researched.[17] Thus, the Department asserts that a card received is a card processed. If, however, it is found by the Court that hours worked includes only the time spent on the telephone, as DialAmerica contends, then Devins admits that his formula would have to be adjusted accordingly.[18]
Devins further testified that if a particular home researcher received 1,000 cards in a given week and neglected to so much as look at 900 of them, the Department would only consider 100 as the number of cards received or processed.[19] However, he added that if a worker at least looked through all of the remaining cards, the time so spent would be included in the calculation of "hours worked."[20]
Upon a thorough review of the deposition testimony of various home researchers, Devins noticed an obvious pattern of minimum wage violations across the board.[21] At a production rate of 60 cards per hour, he found that 91% of the 4,922 person-work weeks in 1982 would have resulted in minimum wage violations. At a production rate of 90 cards per hour, 53% of the person-work weeks resulted in minimum wage *820 violations. Finally, at the rate of 50 cards per hour, every employee was subjected to a minimum wage violation.[22] From his investigation Devins concluded that the lowest rate of cards per hour at which the minimum wage violation would be eliminated for every employee would be 107.[23]
Finally, Devins concluded that there existed a pattern as to how the home researchers performed their work. Workers generally first sorted cards, then screened cards to determine which cards to call, made phone calls, and finally initialed each card. Although some worked 30 minutes at a time and some four hours at a time, Devins is convinced that once the researchers sat down to work, each one performed the same basic tasks in precisely the same manner.[24]

C. Deposition Telephone Tests

DialAmerica offered evidence of telephone tests initiated in conjunction with the depositions of several home researchers for this Court's consideration in determining whether there is a reasonable basis for finding a production rate for the testifying home researchers.
These tests, conducted by DialAmerica, required the deponents to research 20 cards by calling Directory Assistance and requesting telephone numbers as they had previously done in their homes. The deponents utilized a touch tone telephone set up at the offices of DialAmerica, and were required to dial "9" for an outside line, and "1" to begin dialing Directory Assistance outside of New Jersey.[25] The DialAmerica attorneys timed each deponent and subsequently made inquiries as to whether the test was representative of the manner in which he or she performed the work at home, whether the use of the automated response system today made the work go faster, and whether that system made it difficult to obtain more than one listing per directory assistance call.
Most deponents indicated that the process was much quicker at the deposition test, and many suggested that they could not have completed the number of cards per hour at home that were completed during DialAmerica's test.
Finally, the cards provided at the deposition test were from one state, whereas researchers, in reality, were given cards from a variety of states. Since many deponents testified that certain states were faster or slower than others, the critical question to ask is whether these tests provide an accurate representation of the probable production rates achieved at home.
Presumably, DialAmerica submitted evidence of its telephone tests in an effort to show that most of the home researchers had the ability to complete more cards than the records and their testimony indicate. If such a showing were in fact made and accepted, this Court could then determine that the minimum wage violations calculated by compliance officer Devins are grossly overstated and that the "pattern" of minimum wage violations is illusory at best.
This Court refuses, however, to ignore the pattern established by the testimony of so many home researchers and the records submitted in evidence. While it may be true that certain home researchers sporadically could have achieved higher rates of production, an assertion of what they "should" have done begs the question and in no way lessens the wage violations that have been committed by DialAmerica.

D. Bellcorp District Manager

The Department of Labor called Donna Bastien of Bell Communications Research ("Bellcorp") as an expert witness. Bastien maintains the title of district manager for open network architecture and has previously been involved in the management of operator systems and technical studies and *821 consultation in the area of Directory Assistance.[26]
Bastien offered testimony as to the average time spent by an operator on a Directory Assistance call between 1980 and 1982 using microfilm or microfiche Directory Assistance systems. This period, the "average work time," consists of the time that the customer is connected to the particular operator system and the operator is serving that customer.[27] In other words, its duration is measured from the time the operator system identified the operator to whom it would forward the call until the time that operator disconnected from the call.[28] Based on documents in evidence, it can be gleaned that in the early 1980s, the average work time for an operator using a computerized system was 30.5 seconds; for an operator using microfilm or microfiche, 33 seconds; and for an operator using a telephone book, 38 seconds in the early 1980's.[29]
In an attempt to demonstrate that the deposition telephone test of 1987 was not conducted under conditions sufficiently similar to those existing in 1980-83, the Department elicited testimony from Bastien as to the rate of growth of computerized Directory Assistance systems. In 1983, 79 computer systems and three microfilm systems were in existence for the Bell operating companies in the United States.[30] By contrast, in 1980, 35% of Directory Assistance systems were using microfilm or microfiche, 14% were using paper records, and 51% were computerized. During her testimony, Bastien described how a call to Directory Assistance proceeds. Once a caller has dialed the appropriate number of digits (depending on which section of the country one is dialing from, this may be as few as three digits or as many as 10),[31] the call is routed through the telephone network by various "switching systems" and eventually terminates at an operator system. The system requires a certain amount of time in order to locate an available operator but, once found, the operator is attached to the call. When the caller makes an information request, the operator must search for the number or numbers using one of the search mechanisms (microfilm/microfiche, computerized database, or phone book). The operator then provides the number or numbers to the caller manually or by use of a computerized announcement machine (audio response system),[32] and then disconnects from the call.
In terms of the amount of time required to complete a Directory Assistance call, Bastien estimated one second per digit dialed using a rotary phone, and at least half of that time for a caller using a touch tone phone.[33] In addition, 140 milliseconds (.140 seconds) are required for the transmission of each digit dialed.[34] She further explained that there exists a hierarchy of switching machines (i.e., classes) used in the telephone network, including the caller's local machine. A call could conceivably be routed through eight classes before obtaining a connection with an operator.[35] Thus, hypothetically, if a caller must dial an area code plus a seven-digit telephone number (i.e., 10 digits in sum), and 140 milliseconds per digit is required, the call could be routed in 5.6 seconds.[36] Although the witness acknowledged that a shortage of operators or a heavy flow of traffic could cause a caller to wait longer than *822 usual, the normal pre-divestiture procedure required a 5.8 second speed of answer time. In other words, 5.8 seconds was the normal time required to actually get connected to an operator.[37] Therefore, assuming 10 seconds for dialing (one second per digit for a 10-digit call), 5.6 seconds for the call to be routed, 5.8 seconds to get the operator, and approximately 30 seconds for average working time, the average Directory Assistance call could be completed in 51 seconds.[38] The average waiting time could, of course, be extended where the caller requested more than one telephone number from the operator. Before the telephone company began charging for Directory Assistance, there was more flexibility in the amount of requests it would tolerate. In light of the subsequent charge for Directory Assistance and the automated response mechanism, an operator could manually monitor the number of requests permitted.[39]
Assuming a slight overload of requests for Directory Assistance, the speed of answer would naturally be longer, according to Bastien. A 5% overload, for instance, would cause a 10-second delay at most. However, there is no direct proportion among these figures, as a 30% overload would not necessarily indicate a 60-second delay.
Finally, Bastien concluded that the use of the automated response mechanism today requires a caller to spend more time to acquire two listings than the caller would have spent in the early 1980s. Thus, while automation may be less expensive to the telephone company, it is not necessarily quicker.[40]
This Court finds Bastien's testimony credible. Accounting for the dialing process, the routing process, the speed of answer time, and average work time, the Court is satisfied that 51 seconds to complete a Directory Assistance call is a reasonable approximation and entirely compatible with the Secretary's finding of 53 cards/hour as the average number processed by the typical home researcher.

IV. DISCUSSION

A. Fair Labor Standards Act (FLSA)

Pursuant to § 11(c) of the FLSA, 29 U.S.C. § 211(c), every employer is required to make, keep and preserve records of persons employed by it and of the wages, hours and other conditions and practices of employment maintained by it. This duty is imposed upon the employer as employees rarely maintain such records, and it is the employer who is in the position to know and produce the most probative facts regarding the nature and amount of work performed. Anderson v. Mt. Clemens Pottery Co., 328 U.S. 680, 687, 66 S.Ct. 1187, 1192, 90 L.Ed. 1515 (1946).
The production records maintained by DialAmerica include name, date, number of cards received, number of cards for which listings were found, and amount paid. However, there is no record of the number of hours worked by the home researchers, and DialAmerica never required its home researchers to keep track of the number of hours worked. A violation of the record-keeping provisions of the FLSA is, therefore, patently obvious, as the number of hours worked is critical to a determination of the minimum wages due.
Section 6(a) of the Act requires an employer to pay each of its employees an amount not less than the applicable minimum wage times the number of hours worked. 29 U.S.C. § 206(a).[41] This work performance payment must be made on a weekly basis. In other words, each work week stands on its own and payments *823 made in productive and unproductive weeks cannot be averaged together for the purpose of a minimum wage determination.[42] Impliedly, therefore, the speed at which one works is not relevant to the calculation of minimum wage.[43]
The Department contends that the unknown number of hours actually worked by each home researcher can be reconstructed through a formula utilizing such known factors as minimum wage, cards received, and amount actually paid. The Department posits that the application of its theory of proof will permit this Court to ascertain a minimum wage violation for each work week by comparing the home researcher's rate of processing cards to the rate at which the researchers would have been required to process cards in order to earn the minimum wage.
An employee who brings suit under § 16(b) of the Act, 29 U.S.C. § 216(b), for the recovery of unpaid minimum wages must prove that he or she has performed work for which he or she was not properly compensated. Anderson, 328 U.S. at 687, 66 S.Ct. at 1192. "The remedial nature of this statute and the great public policy which it embodies, however, militate against making the burden an impossible hurdle for the employee." Id.
The Anderson case and its progeny establish that when the employer has complied with the Act and has maintained proper and adequate records, the burden of the employee is easily discharged by securing production of those records. Id. However, where, as in the case at bar, the employer's records are inaccurate or inadequate, and the employee alone is unable to offer convincing proof, a serious problem arises. The solution, however, is not to penalize the employee by denying recovery based on an inability to prove the extent of the undercompensated work. Such a result "would place a premium on an employer's failure to keep proper records in conformity with his statutory duty; it would allow the employer to keep the benefits of an employee's labors without paying due compensation as contemplated by the Fair Labor Standards Act." Id. The employee in a case such as this meets the required burden if he or she can prove that work was performed for which the worker was not properly compensated and if he or she produces sufficient evidence to show the "amount and extent of that work as a matter of just and reasonable inference." Id. (emphasis added); see Brock v. Seto, 790 F.2d 1446, 1448 (9th Cir.1986); Donovan v. New Floridian Hotel, Inc., 676 F.2d 468, 472 (11th Cir.1982); Marshall v. Van Matre, 634 F.2d 1115, 1119 (8th Cir.1980).
Once the employee has satisfied this standard, the burden shifts to the employer to produce evidence of work performed or to negate the reasonableness of the inference to be drawn from the employee's evidence. Anderson, 328 U.S. at 687-88, 66 S.Ct. at 1192. If the employer is unable to meet this burden, the Court may determine and award damages to the employee. Id. As the Anderson Court held:
The employer cannot be heard to complain that the damages lack the exactness and precision of measurement that would be possible had he kept records in accordance with the requirements of § 11(c) of the Act.... The employer, having received the benefits of such work, cannot object to the payment for the work on the most accurate basis possible under the circumstances.
Id. at 688, 66 S.Ct. at 1192-93.
After an employee has proved that he or she has performed work for which lesser compensation was received than provided by law, the fact of damage is certain. The uncertainty arises in the determination of the precise amount of damages sustained due to the statutory violation by the employer. Id. In that case, "it would be a perversion of fundamental principles of justice to deny all relief to the injured person, and thereby relieve the wrongdoer from making any amend for his acts." Id. (citing Story Parchment Co. v. Paterson Co., 282 U.S. 555, 563, 51 S.Ct. 248, 250, 75 L.Ed. 544 (1931). "It is enough under *824 these circumstances if there is a basis for a reasonable inference as to the extent of the damages." Id. (citing Eastman Kodak Co. v. Southern Photo Co., 273 U.S. 359, 377-79, 47 S.Ct. 400, 404-05, 71 L.Ed. 684 (1927); Palmer v. Connecticut Ry. Co., 311 U.S. 544, 560-61, 61 S.Ct. 379, 384-85, 85 L.Ed. 336 (1941).
In light of these principles, when the employee has satisfied the burden of proof, the district court must determine the award of damages. The Court is vested with a great deal of discretion in determining the most accurate amount to be awarded. Brock v. Norman's Country Market, Inc., 835 F.2d 823, 828 (11th Cir.1988). In many instances, when FLSA claims are made against employers, the records maintained as to each employee are inadequate or inaccurate. In such cases, the district court must look to the litigants for assistance.[44]Id. "It is for the trial judge to determine from all he has and sees the weight to be accorded the compliance officer's computations." Id. (citing Hodgson v. American Concrete Construction Co., Inc., 471 F.2d 1183, 1186 (6th Cir.1973)). Moreover, it is not imperative that every employee testify in order to make out a prima facie case of the number of hours worked as a matter of "just and reasonable inference," and the fact that several employees do not testify does not vitiate their claim. Id. (citing Donovan v. New Floridian Hotel, Inc., 676 F.2d at 472.
It is incumbent upon this Court to weigh the evidence before it, including the testimony of some 43 home researchers, for the purpose of determining whether a minimum wage violation exists and, if so, whether back wages may be awarded to the testifying, as well as the non-testifying, home researchers formerly employed by DialAmerica.

B. Representative Testimony

A critical issue in this case concerns the use of representative testimony to establish minimum wage violations for approximately 350 non-testifying employees.
In support of its contention that representative testimony cannot be utilized in this case, DialAmerica points to three situations in which such testimony has been accepted:
In one such class of cases there is substantial other evidence to support the inference drawn from the representative testimony.... In each of these cases, evidence in addition to representative testimony was submitted and relied upon by the court in reaching reasonable inferences of FLSA violations and awarding just, though approximate, damages to non-testifying as well as testifying employees.
A second class of cases ... involve[s] an employer systematically causing records to be falsified that would otherwise be properly maintained.
Finally, another class of cases in which reasonable inferences may be drawn from representative testimony involves the establishment by the Department of a uniform pattern or practice of work methods, conditions, and hours encompassing a class of employees.
Defendant's Proposed Findings of Fact and Conclusions of Law, at 9-10 (emphasis added) (citing Brock v. DialAmerica Marketing, Inc., Civil Action No. 81-4020, 1986 WL 28913 (D.N.J. Oct. 15, 1986), slip op. at 4-6).
DialAmerica recognizes that the Department may present representative testimony in any of these three situations to allow the Court to draw inferences regarding the work habits of all former home researchers, both testifying and non-testifying. However, DialAmerica points out the Court's word of caution:
... the Department should realize DialAmerica will have an opportunity to rebut the reasonableness of such inferences. If DialAmerica presents evidence to rebut the reasonableness of an inference that the work habits of the testifying employees are representative of the work habits of non-testifying employees, this Court will not be able to find FLSA violations or award damages to non-testifying *825 employees. Thus, if DialAmerica rebuts the Department's representative testimony, only testifying employees who establish FLSA violations will be able to recover damages.
Defendant's Proposed Findings of Fact and Conclusions of Law, at 11 (citing Brock v. DialAmerica, slip op. at 6).
Despite such warning, DialAmerica contends that the Department has failed to demonstrate a representative pattern among the home researchers and that, in fact, the unique manner in which each worker performed his or her work precludes the use of representative testimony in the home worker scenario.
This Court, however, finds that the Department has successfully demonstrated patterns among home researchers through the testimony of a number of home researchers. The basic research task, for instance, can be performed, and has likewise been described, in only one manner: dial the operator, request a telephone number, record the number, and initial the card.[45] Moreover, every researcher was required to use the Directory Assistance services of the telephone company, and all were uniformly subjected to its limitations in speed of transport of a call, speed of dialing, waiting time for the connection to an operator, and limitations upon the number of listings to be provided by the operator.[46] Thus, although individuals may have chosen to do their research at different times of the day and did not work in each other's presence or under the supervision of DialAmerica, their basic research task was straightforward and uniform.
In addition to the appearance of work patterns, this Court perceives an unrebutted pattern of minimum wage violations by DialAmerica. The law permits reliance upon representative testimony to support the discovery of minimum wage violations and the award of back wages under the FLSA to non-testifying as well as testifying employees. Brock v. Tony & Susan Alamo Foundation, 842 F.2d 1018, 1019-20 (8th Cir.1988); Donovan v. New Floridian Hotel, Inc., 676 F.2d at 471-73.
The district court must "estimate and fashion a reasonable remedy that restores as fully as possible all of the employees covered by the FLSA who were improperly denied compensation" even where the records are deficient. Brock v. Tony & Susan Alamo, 842 F.2d at 1019. In that case the court declared that the exact form of remedy is left to the district court, but "to compensate only those employees who chose or were chosen to testify is inadequate in light of the finding that other employees were improperly denied compensation." Id. at 1019-20.
The testimony of 43 witnesses, both at trial and by deposition, confirms the existence of minimum wage violations for every home researcher employed by DialAmerica between 1980 and 1982. The sheer commonality of their testimony breathes credibility into the claims of the testifying home researchers, and permits this Court to feel comfortable in drawing inferences therefrom.
The majority of those who testified claimed that they were able to process cards at rates falling between 30 and 60 per hour. The average rate for all employees was 53 cards/hour, a number derived by averaging the midpoint rates for all testifying witnesses (Appendix C). Based on the testimony given, this Court finds that the work habits of non-testifying witnesses were sufficiently similar to testifying witnesses. Such a finding allows for a determination of the number of hours worked by those not testifying as a matter of "just and reasonable inference." Anderson, 328 U.S. at 687, 66 S.Ct. at 1192; Donovan, 676 F.2d at 472.
This Court's decision that non-testifying employees are entitled to an award of back wages finds support not only in the testimony of former home researchers, but in the testimony of Compliance Specialist William *826 Devins. Other courts have expressed acceptance of the admissibility of both the testimony and calculations of compliance officers as they pertain to minimum wages due. Brock v. Seto, 790 F.2d 1446, 1449 (9th Cir.1986); Hodgson v. Humphries, 454 F.2d 1279, 1282-83 (10th Cir.1972); Hodgson v. American Concrete Construction Co., Inc., 471 F.2d 1183, 1186 (6th Cir.), cert. denied, 412 U.S. 949, 93 S.Ct. 3007, 37 L.Ed.2d 1001 (1973) ("where, as here, the [compliance officer's] computations of overtime pay were based in part on employer records, those computations were improperly excluded").
In the present scenario, the testimony of Devins constitutes the "substantial other evidence" based upon which this Court may reasonably infer FLSA violations and award damages to non-testifying employees, although the result may be less than precise in its measurement.
The mathematical analysis undertaken by Devins was substantially based upon the business records of DialAmerica and demonstrates in great detail the total extent of DialAmerica's minimum wage violations.[47] Of utmost significance is the proposed formula for the calculation of back wages due. This Court accepts the proposed theory that a card received and sorted is a card processed, and therefore finds Devins' formula to be the most promising for the onerous calculation of back wages due. For each employee in each week, Devins is able to determine whether, based on an assigned rate of cards/hour,[48] number of cards received, and actual pay, a particular employee received the appropriate minimum wage each week.
This Court believes that the assignment of the 53 cards/hour average to each employee will yield the most equitable result in determining the amount of back wages to be awarded to both testifying and non-testifying home researchers. Because DialAmerica has failed to maintain the appropriate records in accordance with the FLSA, it cannot now complain that the damages are inaccurate or inappropriate. Anderson, 328 U.S. at 688, 66 S.Ct. at 1192. Had DialAmerica maintained the proper records, a more precise amount could have been awarded.
Moreover, DialAmerica has failed to rebut the reasonableness of the inferences drawn from the representative testimony presented. The evidence of its deposition telephone test is unconvincing. The test does not represent a realistic reconstruction of the conditions under which the home researchers worked in 1980-82, and thus cannot be used to rebut the testimonial recall of the witnesses. The testimony of its own witnesses,[49] in fact, corroborates the pervasive pattern of minimum wage violations. Although production rates may vary among researchers, this discrepancy is an insufficient basis upon which to deny recovery for employees who establish undercompensation pursuant to the FLSA.
Since an average rate of 53 cards/hour has been ascertained, that average figure may be utilized in conjunction with the formula proposed by Devins for the purpose of determining cards/hour and, thereby, back wages due.

V. REMEDIAL ACTION

A. Injunction

The Department of Labor seeks an injunction restraining future violations of the minimum wage and record-keeping provisions of the FLSA. Injunctions are frequently granted in cases of this nature "because of the significant public interest affected by violations of the FLSA" and because an injunction relieves the Secretary of the burden of administering and enforcing the FLSA. Marshall v. R & M *827 Erectors, Inc., 429 F.Supp. 771, 782 (D.Del. 1977); see Bay Ridge Co. v. Aaron, 334 U.S. 446, 460, 68 S.Ct. 1186, 1194, 92 L.Ed. 1502 (1984); Mitchell v. Robert DeMario Jewelry, Inc., 361 U.S. 288, 80 S.Ct. 332, 4 L.Ed.2d 323 (1960); Schultz v. Wheaton Glass Co., 319 F.Supp. 229, 232 (D.N.J. 1970), aff'd, 446 F.2d 527 (3d Cir.1971).
Moreover, the issuance of a permanent injunction in this case would not subject the employer to a penalty or hardship as it merely requires the employer to comply with the law. See Marshall, 429 F.Supp. at 782.
The crucial question in ascertaining the suitability of injunctive relief is whether the risk that the defendant will fail to keep appropriate employee records or to pay the proper minimum wage is substantial enough to warrant such a remedy. Id. Although DialAmerica has in fact discontinued its home researcher program, it has not abandoned its business completely, and the risk is, therefore, ever present that it will resume the home researcher program at improper rates of pay. Furthermore, without the benefit of an injunction to restrain DialAmerica from further withholding wages, employees granted the right to receive back wages will have no means by which to enforce that right. Wirtz v. Malthor, Inc., 391 F.2d 1, 3 (9th Cir.1968).
In light of these principles, this Court will, therefore, grant the requested injunction to prevent the future violation by DialAmerica of the FLSA minimum wage and recordkeeping provisions.

B. Back Wages

The precise amount of damages to be awarded each home researcher is to be determined on the basis of the formulae presented at trial and the records provided to the Court by both DialAmerica and its former employees. This Court finds that the use of the average production rate of 53 cards/hour for all employees will allow for the most equitable determination of back wages due. As stated previously, had DialAmerica maintained proper records of the hours worked by its employees, a precise calculation of back wages due would have been feasible. However, the unavailability of such data leads this Court to the conclusion that the application of the average production rate (53 cards/hour) will provide the most reasonable approximation.

C. Pre-Judgment Interest

The Third Circuit's recognition of a presumption in favor of pre-judgment interest requires this Court to apply that presumption in the present matter. Brock v. Richardson, 812 F.2d 121, 126-27 (3d Cir.1987). In fact, many of the appellate courts considering this issue have held that pre-judgment interest for back pay awards under the FLSA is mandatory or should be presumed appropriate. Id. at 126 (citing Usery v. Associated Drugs, Inc., 538 F.2d 1191, 1194 (5th Cir.1976); Ford v. Alfaro, 785 F.2d 835, 842 (9th Cir.1986)).

CONCLUSION
A thorough review of the record leads this Court to the following conclusions:
1. DialAmerica has violated both the record-keeping and minimum wage provisions of the FLSA, 29 U.S.C. § 211(c) and § 206(a), by failing to record the hours worked and by undercompensating its employees for work performed.
2. A pattern of minimum wage violations encompassing non-testifying employees has been established through the representative testimony of 43 former home researchers. DialAmerica has failed to rebut the existence of this pervasive pattern.
3. The formulae proposed by the compliance specialist are sufficient to enable a calculation of back wages due every former home researcher based on an average rate of 53 cards/hour.
4. Pre-judgment interest will be appropriately awarded to each home researcher receiving back wages.
5. An injunction against future violations of the minimum wage and recordkeeping provisions of the FLSA is appropriate.
6. Finally, this Court, understanding that further action will be required to implement *828 its decision, directs that all further applications be referred to the Magistrate.
NOTES
[1]  Thus, the instant case is limited to the examination of home researchers who worked within the two-year statutory period (i.e., the award of back wages will only be considered with respect to those who worked after January 1, 1980).
[2]  The years of concern in this case are 1980 to 1982.
[3]  See Stipulation, Exhibit 115, at 22, 25.
[4]  See Exhibit Nos. P-3 and P-4 (Poss' records); P-9 (Milo's records); and P-2 (Catrambone's records).
[5]  Exhibit S-111 (Production Records of DialAmerica) and Exhibit 10 (DialAmerica Payroll Analysis  Cards/Hour Below Which Minimum Wage Exists).
[6]  Tr. 605.
[7]  Tr. 606.
[8]  This formula will yield the proper production rate only if one accepts the Department's assumption that a card received is equivalent to a card processed.
[9]  How this translates into back wages due is calculated in Part IIIB(4), infra.
[10]  Tr. 611, 612.
[11]  These employees are Piper, at 37 cards/hour, a conceivable rate of production; Sarfatty, at 52 cards/hour, who may have had the ability to process cards at such a rate; and Poss, at 43 cards/hour, who could also conceivably have reached such a production rate.
[12]  The witness performed similar mathematical calculations with respect to home researchers operating as distributees, for whom DialAmerica maintained no records. For this purpose, he utilized the records provided by several distributors.
[13]  This formula is based upon the idea that the ratio of the "listed" to the unknown "received" is identical to the ratio of 100% to 37.18%. Tr. 641.
[14]  Setting the minimum wage due equal to the actual amount received reveals the lowest number of cards/hour at which the minimum wage would have been paid.
[15]  Tr. 696-97.
[16]  Tr. 624.
[17]  Devins' statement corroborated the testimony of most of the home researchers.
[18]  Tr. 716.
[19]  Tr. 730.
[20]  Tr. 731.
[21]  Tr. 759.
[22]  Tr. 760.
[23]  Tr. 761.
[24]  Tr. 771.
[25]  The deponents indicated that these steps were not necessary at the time of their home research in 1980-82.
[26]  Tr. 523-24.
[27]  Tr. 529.
[28]  Tr. 556.
[29]  The witness testified that paper and microfilm systems are presently being phased out in favor of the computer, and that the data relied upon for the years 1980-83 may not be completely relevant to the year 1987. Tr. 536.
[30]  Tr. 548.
[31]  Tr. 550.
[32]  The automated response system, not in use until 1982, is one by which the requested telephone number is recited not by the operator manually, but by recording.
[33]  Tr. 559-60.
[34]  Tr. 561.
[35]  Tr. 561-62.
[36]  Tr. 563.
[37]  This 5.8 second goal was reached 98% of the time in 1981, 99% of the time in 1982, and 99% of the time in 1983.
[38]  Tr. 565.
[39]  Another effect of the automated response is that it is not included in average working time. Thus, if an operator chooses to use the automated response rather than an oral response, the average working time is naturally diminished.
[40]  Tr. 578.
[41]  As already noted, in 1980 the minimum wage was $3.10/hour. Subsequently, the minimum wage was raised to $3.35/hour.
[42]  Tr. 808, 816-17.
[43]  Tr. 819.
[44]  Brock, in fact, offered the testimony of a compliance officer to assist the Court.
[45]  While the use of telephone books was mentioned, this was not a common method of research.
[46]  Plaintiff's Proposed Findings of Fact and Conclusions of Law, at 70.
[47]  Devins' complete calculations and the reasons therefor were previously discussed in detail in supra Part III(A) & (B).
[48]  Cards/hour was an unknown figure supplied by the testimony of former home researchers. On average, home researchers were able to research 53 cards per hour.
[49]  Employees testifying at trial on behalf of DialAmerica include Poss, Catrambone, K. Davis, S. Davis, Epstein, Milo, Antonacci, Catannia and Rizzo.
