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CAT-2005-Previous Years Paper
A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs 250 and Rs 300 per day respectively. In addition, a male operator gets Rs 15 per call he answers and female operator gets Rs 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job?
Let us form both the equations first:
40 m + 50f = 1000
250 m + 300 f + 40 × 15 m + 50 × 10 × f = A
850 m + 8000 f = A
Where m and f are the number of males and females and A is the amount paid by the service provider.
Then the possible values for f are 8, 9, 10, 11 and 12
If f = 8, then m = 15
If f = 9, 10, 11 then m will not be an integer while f = 12 then m will be 10.
By putting f = 8 and m = 15, A = 18800. When f = 12 and m = 10 then A = 18100.
Hence, the number of males will be 10.