Question

A rectangular box with a square base of length $x$ and height $h$ is to have a volume of $20 \mathrm{ft}^{3} .$ The cost of the top and bottom of the box is 20 cents per square foot. and the cost for the sides is 8 cents per square foot. Express the cost of the box in terms of a. the variables $x$ and $h$ b. the variable $x$ only; and c. the variable $h$ only. d. Use a graphing device to approximate the dimensions of the box that will minimize the cost.

          A rectangular box with a square base of length $x$ and height $h$ is to have a volume of $20 \mathrm{ft}^{3} .$ The cost of the top and bottom of the box is 20 cents per square foot.
and the cost for the sides is 8 cents per square foot. Express the cost of the box in terms of
a. the variables $x$ and $h$
b. the variable $x$ only; and
c. the variable $h$ only.
d. Use a graphing device to approximate the dimensions of the box that will minimize the cost.

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Added by Alex J.

Precalculus with Limits

Ron Larson 2nd Edition

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Solved by Expert Ekaveera Kumar

04/15/2022

Step 1

Step 1: The cost of the top and bottom of the box is $40X^2$ cents, and the cost for the sides is $32XH$ cents. Show more…

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A rectangular box with a square base of length $x$ and height $h$ is to have a volume of $20 \mathrm{ft}^{3} .$ The cost of the top and bottom of the box is 20 cents per square foot. and the cost for the sides is 8 cents per square foot. Express the cost of the box in terms of a. the variables $x$ and $h$ b. the variable $x$ only; and c. the variable $h$ only. d. Use a graphing device to approximate the dimensions of the box that will minimize the cost.

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