I am not going to do this one for you, but you need to come up with an equation(s) that describe the surface area of the box (in terms of its dimensions). In the end, you want ONE equation in terms of only ONE variable (either length, width, or height). (Hint: length is 4 times height, box has top and bottom, and volume is 40 cubic feet). Once you have this equation, find its derivate.
Then set its derivative equal to zero. Wherever the derivate equals zero there is potential for a max or min. In your case, you are looking for a min ("minimum ammount of plywood required to construct the box"). Find this value, and plug it back in to your original surface area equation. This will give you the minimum square footage of plywood needed to construct your box.