A closed box with a square base is to be manufactured. The material for the top of the box costs $2 per square foot and the material for the remainder of the box costs $1 per square foot. If the total cost per box is to be $48, find the dimnesions of the box with the largest volume. Please include the following steps with appropriate work.  a. a labeled sketch  b. variables defined and labeled on the sketch.  c. a constraint equation for the cost

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