A parcel delivery service will deliver a package only if the length plus girth​ (distance around) does not exceed 72 inches.   ​(A) Find the dimensions of a rectangular box with square ends that satisfies the delivery​ service's restriction and has maximum volume. What is the maximum​ volume?   ​(B) Find the dimensions​ (radius and​ height) of a cylindrical container that meets the delivery​ service's restriction and has maximum volume. What is the maximum​ volume?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 16T
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A parcel delivery service will deliver a package only if the length plus girth​ (distance around) does not exceed 72 inches.
 
​(A) Find the dimensions of a rectangular box with square ends that satisfies the delivery​ service's restriction and has maximum volume. What is the maximum​ volume?
 
​(B) Find the dimensions​ (radius and​ height) of a cylindrical container that meets the delivery​ service's restriction and has maximum volume. What is the maximum​ volume?
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