Question

A rectangular fence is to be built along a river using the river as one side of the fence.the cost of the fencing for the two ends is $8 per sq ft and the cost of the fencing for the side running parallel to the river is $12 per sq ft. If you have $3600 to spend on purchasing the fencing,what are the dimensions of the rectangular fence and the maximum are of the fence?

Answer 1

let each of the two end fences be x ft long
let the side parallel to the river be y ft long

so we have:
cost = 12y + 8(2x) = 12y + 16x
but 12y + 16x = 3600
3y + 4x = 90
y = (90-4x)/3

area = xy = x(90-4x)/3
= 30x - (4/3)x^2
d(area)/dx = 30 - (8/3)x
= 0 for a max of area
(8/3)x = 30
8x = 90
x = 90/8 =11.25 ft
y = 15

check my arithmetic