Answer:
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 [tex]x\ge 0, \ y\ge 0.[/tex]
The grower has 250 acres of land available, then
[tex]x+y\le 250[/tex]
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
[tex]x+2y\le 240[/tex]
The profit is $120 per acre of apples and $215 per acre of peaches, then the total profit is
[tex]P=120x+215y[/tex]
We get the function [tex]P=120x+215y[/tex] which must maximized using restrictions
[tex]\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 250\\ x+2y\le 240\end{array}\right.[/tex]
Show the solution set of this system of inequalities graphically.
The maximum profit can be at the vertices of this region:
[tex]P(0,120)=120\cdot 0+215\cdot 120=\$25,800\\ \\P(240,0)=120\cdot 240+215\cdot 0=\$28,800[/tex]
The maximum profit will be $28,800 when 240 acres go for apples and 0 acres go for peaches
