Answer in Calculus for Amit #262175

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

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\n2y=500-5x\ny=250-(5/2)x”

Maximum area “(A)=xy”

“A=x(250-(5/2)x)\nA=250x-(5/2)x^2”

Diff. w.r.t “x”

“frac{dA}{dx}=frac{d}{dx}(250x- frac{5}{2}x^2)n=250-5x”

For maximum area:

“250-5x=0Rightarrow x=50”

“y=250-(5/2)x=250-(5/2)(50)=125”

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