college Algebra

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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?

  • college Algebra -

    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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