Question

A rancher has 444 feet of fencing to enclose two adjacent rectangular corrals. The wall separating the two

corrals consists of a single fence. What dimensions for one of the individual corrals will produce the largest
total area?

Answer 1

2 lengths and 3 widths

444 = 2*L + 3*w --> L = (444 - 3w)/2 = 222 - (3/2)w

Area = length x width

Area (w) == (222 - (3/2)w ) w

The max occurs at the average of the zeros.

The zeros are 222 - (3/2)w = 0 or w=0

222 = (3/2)w or w=0

w = 444/3=148 or w=0

The average is (444/3 +0)/2 = 222/3=74

width is 74 and length is 222 - (3/2)(74) = 222 - 111 = 111

The max area is 74 * 111 = 8214