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?

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.