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How to solve such an optimization problem efficiently？?

Help! how to solve this optimization problem?

  • Answer:

    You'd need six equal parallel pieces going one way with two other pieces going across. If x = the length of one of the 6 pieces and y = the length of an across piece, the area xy = 18000 so y = 18000/x and the total length of fence 6x + 2y now becomes 6x + 36000/x Its derivative is 6 - 36000/x^2 which equals zero for a minimum, right? So 36000/x^2 = 6 6x^2 = 36000 x^2 = 6000 x = √6000 and y = 18000/√6000

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You'd need six equal parallel pieces going one way with two other pieces going across. If x = the length of one of the 6 pieces and y = the length of an across piece, the area xy = 18000 so y = 18000/x and the total length of fence 6x + 2y now becomes 6x + 36000/x Its derivative is 6 - 36000/x^2 which equals zero for a minimum, right? So 36000/x^2 = 6 6x^2 = 36000 x^2 = 6000 x = √6000 and y = 18000/√6000

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