An open-top box with a square base is to be constructed from two types of materials, one for the bottom and one for the sides. The volume of the...

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There is one bottom with the area `x^2` square feet. Its cost is `4x^2` Pesos. There are also four sides, each of them is a rectangle with one side of the length x and other with the length y. Therefore their combined area is `4xy` and the cost is `3*4xy=12xy` Pesos.

The volume of a box is `x*x*y=x^2 y=9` cubic feet. From this equation we can express `y=9/x^2` feet. This is the answer for the first question.

The total cost of the materials is

`4x^2+12xy=4x^2+12x*9/x^2=4x^2+108/x` (Pesos).

This is the answer for the second question.