A certain airline requires that the total outside dimensions (length + width + height) of a carry-on bag not exceed 58 inches. Suppose you want to carry on a bag whose length is twice its height. What is the largest volume bag of this shape that you can carry on a flight? (Round your answer to the nearest integer.)

Question

Parker Clements

Mathematics

31 January, 16:01

A certain airline requires that the total outside dimensions (length + width + height) of a carry-on bag not exceed 58 inches. Suppose you want to carry on a bag whose length is twice its height. What is the largest volume bag of this shape that you can carry on a flight? (Round your answer to the nearest integer.)

+3

Answers (1)

Know the Answer?

Alena Wood · Answer 1

L+W+H=58 and L=2H, then: 2H+W+H=58 - - - > 3H+W=58 or W=58-3H

Volume V=L·W·H = (2H) · (58-3H) H=116H^2-6H^3

We make its first derivative equal to 0:

232H-18H^2=0---> two solutions: H=0 (discarded) and H=232/18

Now the volumen will be: 116· (232/18) ^2-6· (232/18) ^3=6423 cubic inches

It is a máximum as the second derivative 232-36H is <0 for H=232/18