CAT 2005 Question Paper Question 28

Question 28

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 a 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 x be no. of male and y be no. of female operators.
We have 40x+50y=1000 .
So x = 25-(5*y/4) also 7<=y<=12.
So y can be 8 or 12.
If y=8 then x=15 and y=12 then x=10 .
Then we have to find total cost incurred in both the cases.
We find that cost is minimum in 2nd case when no. of males are 10.

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