Answer
$x=\frac{500}{3}\approx166.7\ ft$, $y= 125\ ft$
maximum area $\frac{62500}{3}\approx20833.3\ ft^2$
Work Step by Step
Step 1. Using the figure given in the exercise, the total length of the fence can be expressed as $3x+4y=1000$, which gives $y=250-\frac{3}{4}x$
Step 2. The area is given by $A=xy=x(250-\frac{3}{4}x)=-\frac{3}{4}x^2+250x$
Step 3. We can find the maximum of the area at
$x=\frac{250}{3/2}=\frac{500}{3}\approx166.7\ ft$
which gives $y=250-\frac{3}{4}(\frac{500}{3})=125\ ft$
Step 4. The maximum area can be found as
$A=\frac{500}{3}\times125=\frac{62500}{3}\approx20833.3\ ft^2$
