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Shipping crates A square-based, box-shaped shipping crate
Chapter 7, Problem 13E(choose chapter or problem)
A square-based, box-shaped shipping crate is designed to have a volume of \(16 \mathrm{ft}^{3}\). The material used to make the base costs twice as much (per \(\mathrm{ft}^{2}\)) as the material in the sides, and the material used to make the top costs half as much (per \(\mathrm{ft}^{2}\)) as the material in the sides. What are the dimensions of the crate that minimize the cost of materials?
Questions & Answers
QUESTION:
A square-based, box-shaped shipping crate is designed to have a volume of \(16 \mathrm{ft}^{3}\). The material used to make the base costs twice as much (per \(\mathrm{ft}^{2}\)) as the material in the sides, and the material used to make the top costs half as much (per \(\mathrm{ft}^{2}\)) as the material in the sides. What are the dimensions of the crate that minimize the cost of materials?
ANSWER:Solution Step 1: We have given the volume of a square based shipping crate; V=16ft 3 The objective is to find the dimension of the crate that minimize the cost of material the volume of a square based shipping crate; 2 V=l h V h = l h = 162 l