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Optimization with Constrained Function 
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#1
Jun409, 11:33 AM

P: 9

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
Jun409, 12:33 PM

Mentor
P: 21,215

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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