CPM Homework Help : PC Problem 7-112

Horizontal rectangle divided into 3 equal vertical pieces. A rectangular pen is to be constructed with three sections as shown in the diagram. If the total amount of fencing available is $500$ feet, what is the maximum area that can be enclosed by the fence? (It is not necessary for the three sections to have equal areas.)

Step 1:

Label the diagram.

Step 2:

Write an equation for the perimeter and the available $500$ feet of fencing. Solve for $y$ .

Same horizontal rectangle, top & bottom, each labeled, y, each of the 4 vertical sides & segments, labeled, x.

Step 3:

Write an equation for the area in terms of $x$ and $y$ .

Step 4:

Substitute the expression for $y$ from the perimeter equation into the area equation.

Step 5:

Use your calculator to graph the area function.