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Question 5: We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/square foot, and the material used to build the sides cost $6/ square foot. If the box must have a volume of 50 cubic feet, what are the dimensions that will minimize the cost to build the box? What is minimum cost to build the box? Illustrate with a labelled diagram.

Question 5: We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/square foot, and the material used to build the sides cost $6/ square foot. If the box must have a volume of 50 cubic feet, what are the dimensions that will minimize the cost to build the box? What is minimum cost to build the box? Illustrate with a labelled diagram.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Draw the diagram

2. Calculate the equation for the volume of the box

3.  Determine the constraint

4. Calculate equation for the cost of making the box 

5.  Find the first derivative of the cost of the box

6.  Find the critical points

7. Determining the dimensions and cost 

8. Give a therefore statement

Question 5: We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/square foot, and the material used to build the sides cost $6/ square foot. If the box must have a volume of 50 cubic feet, what are the dimensions that will minimize the cost to build the box? What is minimum cost to build the box? Illustrate with a labelled diagram.
Transcribed Image Text:Question 5: We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/square foot, and the material used to build the sides cost $6/ square foot. If the box must have a volume of 50 cubic feet, what are the dimensions that will minimize the cost to build the box? What is minimum cost to build the box? Illustrate with a labelled diagram.
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