Cedar plank math question
- Suppose you have a cedar plank of length 36 inches and width 3 inches. For the purpose of this problem, suppose the thickness of wood is negligible.
- If you use this plank for the sides of the box only, find the dimensions of the largest (in terms of volume) rectangular bentwood box that you can make.
- Would your answer to part a) change if the width of the plank was different? Explain why or why not.
- Suppose now that you want to use this plank to make the sides and the bottom of the box. You are only allowed to make one cut to cut off a piece of the plank for the bottom of the box; you will then bend the rest of the plank to form the sides of the box. Find the dimensions of the largest (in terms of volume) bentwood box that you can make.