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CALCULUS

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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 - ,

    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 - ,

    thank u sooo much

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