Question

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 $4.20 per square foot to build the base and $0.75 per square foot to build the sides. Write the cost C ofconstructing the box as a function of x, y, and z.

Answer 1

`C(x,y,z) = 4.2xy + 1.5xz + 1.5yz`

Explanation:

We are given the following information in the question:

A rectangular box has a length of x feet, a width of y feet, and a height of z feet.

Area of base =

`\text{Length}* \text{Base}\\=x* y`

Cost of building base = $4.20 per square foot

Total cost of building base =

`\text{Area of base}* 4.20\\= 4.2xy`

Area of 4 walls =

`2(\text{Length}* \text{Height} + \text{Base}* \text{Height}) \\=2(xz+yz)`

Cost of building base = $0.75 per square foot

Total cost of building 4 walls =

`\text{Area of 4 walls}* 0.75\\= 1.5(xz+yz)`

Total cost of building box =

`C(x,y,z) = 4.2xy + 1.5(xz+yz)\\C(x,y,z) = 4.2xy + 1.5xz + 1.5yz`