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djverab [1.8K]
3 years ago
14

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.
Mathematics
1 answer:
daser333 [38]3 years ago
7 0

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

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