Homework Help: CALCULUS

Posted by JENNY on Tuesday, March 30, 2010 at 7:25pm.

gardner wishes to encloe a rectangular 3000 square feet area with bushes on three sides and a fence on the 4th side .If the bushes cost $25.00per foot and the fence costs $10.00 per foot, find the dimensions that minimize the total cost and find the minimum cost

CALCULUS - Reiny, Tuesday, March 30, 2010 at 7:40pm
let the length be x feet, and the width be y feet
we know xy = 3000
so y = 3000/x

You don't say if the fence is along the length or along the width.
I will work it as if it the length has the fence.
If otherwise, just go through it again by changing the equation.

Cost = 10x + 10y + 25(2y)
= 10x + 60y
= 10x + 60(3000/x)
d(cost)/dx = 10- 180000/x^2 = 0 for a minimum Cost
10 = 180000/x^2
x^2 = 18000
x = 134.16
y = 3000/x = 22.36
minimum cost = 10(134.16) + 60(22.36) = 2683.28
CALCULUS - JENNY, Tuesday, March 30, 2010 at 8:59pm
thank u sooo much

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