A homeowner plans to enclose a 200 square foot rectangular playground in his garden, with one side along the boundary of his property. His neighbor will pay for one third of the cost of materials on that side. Find the dimensions of the playground that will minimize the homeowner’s total cost for materials. Follow the steps:
Let the width to be y and the length (the side along the boundary of his property) to be x, and assume that the material costs $1 per foot. Then the quantity to be minimized is (expressed as a function of both x and y) C=

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