Acertain 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.)

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