In this question, you will work step-by-step through an optimization problem. many airlines restrict the size of carry on item in terms of their combined length, width and height (l w h). i am due to fly on an airline that states "the sum of the length, the width and height of your item must be at most 40 inches". suppose i want to take a box (cuboid) on my trip that will allow me to carry on as much as possible, and that i also want this box to have a square base. the questions we will answer using optimization are: what dimensions should the box have, and what would be the resulting maximum volume