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?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 13T
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Numbers 4 and 5. Answer both please.

6:07
< Вack
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
Calendar
Тo Do
Notifications
Inbox
Transcribed Image Text:6:07 < Вack 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 Calendar Тo Do Notifications Inbox
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