A rectangular box with an open top has a length of x feet, a width of y feet, and a height of z feet. It costs $2.10 per square foot to build the base and $0.75 per square foot to build the sides. Write the cost C of constructing the box as a function of x, y, and z.

Question

Quizplus · Accepted Answer

The surface area of the base is xy, so the cost to build the base is 2.10(xy) = 2.10xy.
The surface area of one side of the box is yz, so the cost to build one side is 0.75(yz) = 0.75yz.
There are two sides, so the total cost to build the two sides is 2(0.75yz) = 1.5yz.
Similarly, the total cost to build the other two sides is also 1.5yz.
The total cost to construct the box is the sum of the cost to build the base and the cost to build the sides, i.e.,
C(x,y,z) = 2.10xy + 1.5yz + 1.5yz = 2.10xy + 3yz.

A Rectangular Box with an Open Top Has a Length