Question

A certain airline requires that the total outside dimensions (length + width + height) of a carry-on bag not exceed 34 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.)

Answer 1

L + W + H = 34

3H + W = 34

W = 34-3H

V = LHW = (2H)(H)(34-3H) = 68 H^2 -6 H^3

extreme value at dV/dH = 0 = 136 H - 18H^2 so divide by H
or 18 H = 136
H= 7.6
W = 11.3
L = 15.2
L+W+H = 34.1 close enough, error due to rounding
LWH = 1305

check that this is a maximum
(d/dH)(dV/dH) = 136-36H = -138<0 yes and good night.