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6 July, 14:04

A farmer plans to plant two crops, A and B. The cost of cultivating Crop A is $40/acre whereas the cost of cultivating Crop B is $60/acre. The farmer has a maximum of $7400 available for land cultivation. Each acre of Crop A requires 20 labor-hours, and each acre of Crop B requires 25 labor-hours. The farmer has a maximum of 3300 labor-hours available. If she expects to make a profit of $170/acre on Crop A and $210/acre on Crop B, how many acres of each crop, x and y, respectively, should she plant in order to maximize her profit?

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  1. 6 July, 15:26
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    We will plant 165 of Crop A

    Explanation:

    We will compare the marginal contribution for each crop: A B

    Profit: 170.00 210

    cost of cultivating: 40.00 60

    CM per constrain 4.25 3.50

    Crop A is better regarding cultivating cost.

    Now we analize the labor hours:

    Profit: 170 210

    Labor hours per crop 20 25

    CM per constrain 8.50 8.40

    Because Crop A is better at both constrain resource It will be better to plant only Crop A if possible. As assigning to Crop B will diminish the return on the scarce resourse.

    We will see how much can we plant of Crop A

    7400 / 40 = 185

    3300 / 20 = 165

    We will plant 165 of Crop A

    which is the maximun we can plant at the given labor hours.
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