A rectangular dog pen is to be made to enclose an area of 22

A rectangular dog pen is to be made to enclose an area of 225 square feet. If x represents the width of the pen, express the total length L of the fencing material required for the pen in terms of x. Considering the physical limitations, find the domain of the function L. Find the dimensions of the pen that will require the least amount of fencing material.

Solution

a ) x --- width of pen ; L ---total length of fencing

Now length of pen = Area/ width = 225/x

So, L= 2*length +2*width = 450/x +2x

b) L = 450/x +2x

Domain x should not be equal to zero

So, (- inf, 0) U( 0, inf)

c) Fo least amount of fencing L shpould be minimum

find L\'(x) =0 ; -450/x^2 +2 =0

x = 15

width = 15 feet ; length = 225/15 = 15 feet