A rectgangular field is to be enclosed by a fence. An existing fence will form one side of the enclosure. The amount of new fence bought for the other three sides is 1200 ft. What is the maximum area of the enclosed field?

Question

anonymous · Answer

Solve the following equation for L:
2 w + L =1200
L = 1200 - 2 w
and replace that value of L in the equation for the area.
A = L w
A = (1200 - 2 w)w
Take the derivative of the above with respect to w and solve the result for w:
0 = 1200 - 4 w
w = 300
Maximum area is:
A = (1200 - 2*300) 300 = 180,000 square feet
The ratio of the length to the width is 2 to 1