A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 31¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 19¢/square foot, determine the dimensions of the box that can be constructed at minimum cost.

Question
Asked Oct 18, 2019

A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 31¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 19¢/square foot, determine the dimensions of the box that can be constructed at minimum cost.

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Expert Answer

Step 1

Given:

Volume 20 ft
Material cost for base = 31¢ per square foot
Material cost for side = 10¢ per square foot.
Material cost for top = 19¢ per square foot
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Volume 20 ft Material cost for base = 31¢ per square foot Material cost for side = 10¢ per square foot. Material cost for top = 19¢ per square foot

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Step 2

Let the length, width and height of the rectangular box be x, x and y respectively. Then,

Volume 20
xy20
20
y=-
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Volume 20 xy20 20 y=-

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Step 3

The total cost is...

С-2(2ху)x10+ хx31+x x19
800х
+31x? + 19х?
800
+50x
х
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С-2(2ху)x10+ хx31+x x19 800х +31x? + 19х? 800 +50x х

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Math

Calculus