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A rectangular box is to have a square base and a volume of 81 ft3. If the material for the base costs $0.32/ft2, the material for the sides costs $0.09/ft2, and the material for the top costs $0.22/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost

A rectangular box is to have a square base and a volume of 81 ft3. If the material for the base costs $0.32/ft2, the material for the sides costs $0.09/ft2, and the material for the top costs $0.22/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 26E
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Minimizing Packaging Costs

 A rectangular box is to have a square base and a volume of 81 ft3. If the material for the base costs $0.32/ft2, the material for the sides costs $0.09/ft2, and the material for the top costs $0.22/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost. (Refer to the figure below.)
A closed rectangular box has a length of x, a width of x, and a height of y.
x= fty= ft
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