A container for wooden matches consists of an open-topped box(to contain the matches) that slides into an outer box, open at both ends. The length of the boxes is fixed at 10cm to match the length of the matches. The outer box is designed so that one side completely overlaps for gluing.
a) if the outer box is made from a sheet of cardboard that is 16cm by 10cm, what dimensions for the outer box will maximize the capacity?
b) What size shoudl the sheet of the cardboard be, to make the inner box in this case?