The grower has 250 acres of land available to raise 2 crops, apples and peaches. it takes 1 day to fertilize an acre of apples and two days to fertilize 1 acre of peaches. there are 240 days a year available for fertilizing. find the number acres of each fruit that should be planted to maximize profit. assuming that the profit is $120 per acre of apples and $215 per acre of peaches. find the constants.

The maximum profit will be $28,800 when 240 acres go for apples and 0 acres go for peaches

Step-by-step explanation:

Let x be the number of acres with apples and y be the numbere of acres with peaches. Note that

The grower has 250 acres of land available, then

It takes 1 day to fertilize an acre of apples, so it takes x days to fertilize x acres of apples.

It takes 2 days to fertilize 1 acre of peaches, so it takes 2y days to fertilize y acres of peaches.

There are 240 days a year available for fertilizing, so

The profit is $120 per acre of apples and $215 per acre of peaches, then the total profit is

We get the function which must maximized using restrictions

Show the solution set of this system of inequalities graphically.

The maximum profit can be at the vertices of this region:

The maximum profit will be $28,800 when 240 acres go for apples and 0 acres go for peaches