4. A closed box with a square base is to have a volume of 16,000 cubic centimeters. The material for the top and the bottom of the box costs $3 per square centimeter, while the material for the sides cost $1.50 per square centimeter. Find the dimensions of the box that will lead to minimum total cost. What is the minimum total cost?
4. A closed box with a square base is to have a volume of 16,000 cubic centimeters. The material for the top and the bottom of the box costs $3 per square centimeter, while the material for the sides cost $1.50 per square centimeter. Find the dimensions of the box that will lead to minimum total cost. What is the minimum total cost?
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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Numbers 4 and 5. Answer both please.

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4_7_optimization.docx
3. A rectangular open top storage tank made with a square base
is to have a volume of 708 cubic feet. Material for the base costs
$6 per square foot, and that for the sides costs $2 per square
foot. What dimensions will minimize the cost of the materials?
4. A closed box with a square base is to have a volume of
16,000 cubic centimeters. The material for the top and the
bottom of the box costs $3 per square centimeter, while the
material for the sides cost $1.50 per square centimeter. Find the
dimensions of the box that will lead to minimum total cost.
What is the minimum total cost?
5. A printer receives an order to produce a rectangular poster
containing 648 square centimeters of print surrounded by
margins of 2 centimeters on each side and 4 centimeters on the
top and bottom. What are the dimensions of the smallest piece of
paper that can be used to make the poster?
4
135
000
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