# college Algebra

posted by Tom

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?

1. Reiny

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

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