Discussion

Question:

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?

Explanation:

Let us calculate the cost per call for a male and a female.

Male: A male can make 40 calls/day.
Total cost = 250 + 15 × 40 = 850
∴ Cost/call for a male = 850/40 = Rs. 21.25

Female: A female can make 50 calls/day.
Total cost = 300 + 10 × 50 = 800
∴ Cost/call for a female = 800/50 = Rs. 16

Hence, it could be cost effective to employ as many females as possible.

We have maximum 12 females who can make 12 × 50 = 600 calls/day.

Remaining (1000 - 600 =) 400 calls should be made by males.
∴ Number of males to be employed = 400/40 = 10 males.

Alternately,
Let x females and y males be employed.

As the total number of calls to be answered = 1000 and males and females can handle 40 and 50 calls respectively everyday

50x + 40y = 1000
40y = 1000 – 50x
∴ y = 25 – x – x/4

As 7 < x ≤ 12, x can be 8 or 12.
If x = 8, y = 15 and if x = 12, y = 10

The total cost of employing x females and y males
= 300x + 250y + (50 × 10 × x) + (40 × 15 × y)
= 800x + 850y

If x = 8 and y = 15, cost = Rs. 19,150
If x = 12 and y = 10, cost = Rs. 18,100

Thus, cost is minimized when the number of male operators is 10.

Hence, option (d).

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