A company produces two products, A and B. The company has 5000 kg of raw material and 2000 hours of labour available. It takes 4 kg of raw material and 5 hours of labour to produce one unit of product A, and 5 kg of raw material and 3 hours of labour to produce one unit of product B. If the profit per unit of A is Rs. 10 and the profit per unit of B is Rs. 8, what is the maximum profit that can be earned?

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Rs. 10000

Rs. 11000

Rs. 8000

Rs. 9000

answer is C.

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Detailed Solution

We can set up the following linear programming problem:

Maximize Z = 10A + 8B
Subject to:
4A + 5B ≤ 5000 (Raw material availability)
5A + 3B ≤ 2000 (Labour availability)
A, B ≥ 0

Solving this problem, we get the optimal production mix to be A = 625 units and B = 250 units, with a maximum profit of Z = 10(625) + 8(250) = Rs. 10000. Therefore, the answer is (c) Rs. 10000.

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