Answer to Question #262175 in Calculus for Amit

Question

Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen 

Answer 1

Diagram is missing.

Adding diagram of the problem:

Solution:

Let , width be $x$ and length be $y$ .

The total amount of fencing is given by

$500=5x+2y\\ 2y=500-5x\\ y=250-(5/2)x$

Maximum area $(A)=xy$

$A=x(250-(5/2)x)\\ A=250x-(5/2)x^2$

Diff. w.r.t $x$

$\frac{dA}{dx}=\frac{d}{dx}(250x- \frac{5}{2}x^2) =250-5x$

For maximum area:

$250-5x=0\Rightarrow x=50$

$y=250-(5/2)x=250-(5/2)(50)=125$

Hence, width is 50 ft and length is 125 ft.