Question

Algebra 2 Math problem (help me its for my final!)

Answer 1

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

`\begin{gathered} x+y\leq70\rightarrow(1) \\ x\ge0\rightarrow(2) \\ y\ge0\rightarrow(3) \end{gathered}`

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

`20x+60y\leq3000`

Divide each term by 10 to simplify the inequality

`2x+6y\leq300\rightarrow(4)`

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.

`P=150x+50y`

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

`\begin{gathered} x+y\leq70 \\ x\ge0 \\ y\ge0 \\ 2x+6y\leq300 \end{gathered}`