Question

find the coordinates of the ordered pair where the maximum value occurs for equation P equals 5 x + 5y + 42 given these constrains

Answer 1

Given the equation:

`P=5x+5y+42`

Given the constraints:

`\begin{gathered} -2x+4y\ge-4 \\ x\ge-8 \\ y\le9 \end{gathered}`

Let's find the ordered pair where the maximum value occurs for P.

From the inequality of let's solve for x and y.

At x = -8:

`\begin{gathered} -2x+4y=-4 \\ -2(-8)+4y=-4 \\ \\ 16+4y=-4 \\ \\ \text{Subtract 16 from both sides:} \\ 16-16+4y=-4-16 \\ 4y=-20 \\ \\ \text{Divide both sides by 4:} \\ (4y)/(4)=(-20)/(4) \\ \\ y=-5 \\ \\ \text{Thus, we have the points:} \\ (x,y)\Longrightarrow(8,-5) \end{gathered}`

At y = 9:

`\begin{gathered} -2x+4y=-4 \\ -2x+4(9)=-4 \\ -2x+36=-4 \\ \\ \text{Subtract 36 from both sides:} \\ -2x+36-36=-4-36 \\ -2x=-40 \\ \\ \text{Divide both sides by -2:} \\ (-2x)/(-2)=(-40)/(-2) \\ \\ x=20 \\ \\ \text{thus, we have the point:} \\ (x,y)\Longrightarrow(20,9) \end{gathered}`

Input the values of x and y into the equation and solve for evaluate for P.

• (x, y) ==> (-8, -5):

P = 5x + 5y + 42

P = 5(-8) + 5(-5) + 42

P = -40 - 25 + 42

P = -23

• (x, y) ==> (20, 9):

P = 5x + 5y + 42

P = 5(20) + 5(9) + 42

P = 100 + 45 + 42

P = 187

We can see the maximum value of P is 187 at (20, 9)

The maximum value occurs at (20, 9)

• ANSWER:

(20, 9)