2 At the beginning of each period, a company must determine how many units to produce. A setup cost of $5 is incurred during each period in which production takes place.

The production of each unit also incurs a $2 variable cost.

All demand must be met on time, and there is a $1 per-unit holding cost on each period’s ending inventory. During each period, it is equally likely that demand will equal 0 or 1 unit.

Assume that each period’s ending inventory cannot exceed 2 units.

a Use dynamic programming to minimize the expected costs incurred during three periods. Assume that the initial inventory is 0 units.

b Now suppose that each unit demanded can be sold for $4. If the demand is not met on time, the sale is lost.

Use dynamic programming to maximize the expected profit earned during three periods. Assume that the initial inventory is 0 units.

c In parts

(a) and (b), is an (s, S) policy optimal?