Question

A fruit grower has 150 acres of land available to raise two crops, A and B. It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B, and there are 240 days per year available for trimming. It takes 0.3 day to pick an acre of crop A and 0.1 day to pick an acre of crop B, and there are 30 days available for picking. The profit is $140 acre for crop A and $235 per acre for crop B. How many acres of each crop should the fruit grower plant in order to obtain maximum profit?

Answer 1

To find the acres of each crop that should be planted in order to obtain maximum profit, set up a system of equations using the given information. Solve the system of equations to find the values of x and y that give us the maximum profit.

Step-by-step explanation:

To find the acres of each crop that should be planted in order to obtain maximum profit, we need to set up a system of equations. Let's assume x represents the number of acres of crop A and y represents the number of acres of crop B.

The total time available for trimming is 240 days. Since it takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B, we can set up the equation: x + 2y = 240.

The total days available for picking is 30 days. Since it takes 0.3 day to pick an acre of crop A and 0.1 day to pick an acre of crop B, we can set up the equation: 0.3x + 0.1y = 30.

The profit per acre for crop A is $140 and for crop B is $235. The total profit can be calculated using the equation: 140x + 235y.

We can now solve the system of equations to find the values of x and y that give us the maximum profit.