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

Answer:

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

Step-by-step 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 =

$\text{Length}\times \text{Base}\\=x\times y$

Cost of building base = $4.20 per square foot

Total cost of building base =

$\text{Area of base}\times 4.20\\= 4.2xy$

Area of 4 walls =

$2(\text{Length}\times \text{Height} + \text{Base}\times \text{Height}) \\=2(xz+yz)$

Cost of building base = $0.75 per square foot

Total cost of building 4 walls =

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

Total cost of building box =

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