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 box is to be 9 cubic feet. The cost of the material for the bottom is 4 Pesos per square foot, and the cost of the material for the sides is 3 Pesos per square foot. Let x be the length of the edge of the square base and let y be the height of the open box.Express the Height of the box in terms of x. Express the cost of the materials in terms of the edge x of the base

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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.