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Optimization with Constrained Function

  1. Jun 4, 2009 #1
    1. The problem statement, all variables and given/known data
    1000m^2 garden. 3 sides made of wooden fence. 1 side made of vinyl(costs 5x as much as wood).

    Length cannot be more than 30% greater than the width.

    Find the dimensions for the minimum cost of the fence.

    2. Relevant equations
    1000 = LW
    C = 2L + W + 5W

    3. The attempt at a solution
    Attempted ignoring the restriction. Answer does not meet restriction. Solved algebraically for the only rectangle where L = 1.3W and L = 1000/W. It is a calculus question and it is therefore suspected that this is not the answer. The minimum cost is not necessarily when the vinyl side is minimal.
  2. jcsd
  3. Jun 4, 2009 #2


    Staff: Mentor

    I would start it this way: Solve the equation LW = 1000 for one variable, say W. Then write your cost function as a function of W alone. Use calculus techniques to find the minimum cost over the interval that includes all possible values of W, given the constraint that the length can't exceed 130% of the width.
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