SOLUTION: A closed rectangular box is to be constructed with a square base. The material for the top costs $2 per square foot whereas the material for the remaining sides costs $1 per square

Question 760994: A closed rectangular box is to be constructed with a square base. The material for the top costs $2 per square foot whereas the material for the remaining sides costs $1 per square foot. If the total cost to construct each box is $36, express the volume of the box in terms of the width of the base.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
The square bottom and top have a side length, w. The rectangular box is height h. Using w and h, the volume of the box is this:

The volume will also depend on the cost of the six sides making the box.
Top: dollars
Bottom: dollar
One side:
Cost of the box: ______see the factor 4 for the four sides.

We want v as a function of w. We can get this solving the cost equation for h.

______________Next, substitute this for h in the volume equation, v.

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