A rectangular box with a square base has a volume of 4 cubic feet. The material for the bottom of the box costs $3 per square foot, the top costs $2 per square foot, and the four sides cost $5 per square foot.
(a) If x is the side length of the square base, and y is the height of the box, find the total cost of the box as a function of one variable.
(b) Find the critical number of the cost function.
(c) Use the Second Derivative Test to show that the critical number for cost is a local minimum.
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