Mathematics, 05.05.2020 17:12 mariaveliz2201
A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material for the sides costs $0.10/ft2, and the material for the top costs $0.13/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.
a. length ft
b. width ft
c. height ft
Answers: 2
, the material for the sides costs 
, and the material for the top costs 
.
![C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2](/tpl/images/0640/6078/cbc46.png)
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A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base cost...
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