Let the number of acres of potatoes is x and the number of acres of corn is y.
Since there are 70 acres to plant, then
[tex]\begin{gathered} x+y\leq70\rightarrow(1) \\ x\ge0\rightarrow(2) \\ y\ge0\rightarrow(3) \end{gathered}[/tex]
Since the cost of each potatoes acre is $20
Since the cost of each corn acre is $60
Then multiply x by 20 and y by 60 to find the cost of them
Since the farmer put aside $3000 to spend on them, then
Add the cost of both and equate the sum by 3000
[tex]20x+60y\leq3000[/tex]
Divide each term by 10 to simplify the inequality
[tex]2x+6y\leq300\rightarrow(4)[/tex]
Since the profit of each acre of potatoes is $150
Since the profit of each acre of corn is $50
Then to find the total profit, multiply x by 150 and y by 50, then sum the products up.
[tex]P=150x+50y[/tex]
The variables are x and y
x represents the number of potatoes acres
y represents the number of corn acres
The objective function is P = 150x + 50y
The system of inequalities is
[tex]\begin{gathered} x+y\leq70 \\ x\ge0 \\ y\ge0 \\ 2x+6y\leq300 \end{gathered}[/tex]
