Question

A telecom provider hires male and female operators to answer 1000 calls/day. Male can handle 40 calls/day, female 50. Fixed pay: Rs. 250 (male), Rs. 300 (female). Per call pay: Rs. 15 (male), Rs. 10 (female). Must employ more than 7 of the 12 females available. How many male operators minimize cost?

• A. 15
• B. 14
• C. 12
• D. 10

Hint:

Set up linear constraints, then minimize cost using allowed bounds.

Answer 1

The Correct Option is D

Let $m$ = male, $f$ = female. Constraints: $40m + 50f = 1000$, $f>7$, $f \leq 12$. Cost = $250m + 15(40m) + 300f + 10(50f) = 850m + 800f$. Minimize cost → minimize $m$ for given constraints. From equation: $m = \frac{1000 - 50f}{40}$. For $f=8$, $m=10$. Cost check shows minimum. \[ \boxed{10} \]