A company makes two products, X and Y, which requires two types of machines. The company has two machines of each type. Each unit of X requires 3 hours on machine 1 and 2 hours on machine 2, while each unit of Y requires 4 hours on machine 1 and 1 hour on machine 2. Each machine can operate for 12 hours per day. If the profit on each unit of X is Rs. 5 and that of each unit of Y is Rs. 4, what is the maximum profit that the company can earn?

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Rs. 18

Rs. 20

Rs. 24

Rs. 22

answer is C.

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Detailed Solution

Let x be the number of units of product X produced and y be the number of units of product Y produced.

The objective function is Z = 5x + 4y (to maximize the profit).

The constraints are:

3x + 4y ≤ 24 (due to the constraint on the hours of machine 1)
2x + y ≤ 12 (due to the constraint on the hours of machine 2)
x, y ≥ 0 (non-negativity constraint)

Solving the above system of inequalities using graphical method or simplex method, we get the optimal solution at (x, y) = (2, 4), with maximum profit Z = 5(2) + 4(4) = Rs. 22.

Therefore, the correct answer is (c) Rs. 22.

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