A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.16/ft2, the material for the sides costs $0.10/ft2, and the material for the top costs $0.14/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 23E
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Minimizing Packaging Costs

 A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.16/ft2, the material for the sides costs $0.10/ft2, and the material for the top costs $0.14/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.

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 A rectangular box is to have a square base and a volume of 63 ft3. If the material for the base costs $0.40/ft2, the material for the sides costs $0.12/ft2, and the material for the top costs $0.16/ft2, determine the dimensions (in ft) of the box that can be constructed at minimum cost.

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