Optimization with Constrained Function

  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. Mark44

    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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