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A farmer has 600 acres of land and wants to grow two crops, wheat and corn, to maximize profit. The profit per acre of wheat is Rs. 2000 and the profit per acre of corn is Rs. 1500. The labor required to grow one acre of wheat is 6 hours and the labor required to grow one acre of corn is 4 hours. The farmer has a maximum of 1200 hours of labor available. Formulate the linear programming problem to determine the optimal crop mix. What is the optimal cropt mix?

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$(300, 300)$

$(200, 400)$

$(200, 600)$

$(600, 600)$

answer is A.

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Detailed Solution

Let x be the number of acres of wheat grown.
Let y be the number of acres of corn grown.

The objective function, to be maximized, is given by:

Z = 2000x + 1500y

The constraints are:

6x + 4y <= 1200 (labor)
x + y <= 600 (land)
x >= 0, y >= 0

The linear programming problem can be solved graphically or by using the simplex method. The optimal crop mix is x = 200 and y = 400, with a maximum profit of Rs. 800,000.

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