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 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?
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Set up linear constraints, then minimize cost using allowed bounds.
Updated On: Jul 31, 2025
- 15
- 14
- 12
- 10
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The Correct Option is D
Solution and Explanation
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.
\[
\boxed{10}
\]
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