A rancher has 444 feet of fencing to enclose two adjacent rectangular corrals.

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 between them. What dimensions for one of the individual corrals will produce the largest total area? What is the maximum area for the two corrals combined?

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