Please explain the solution

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-enit bolding 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 programining 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? 3 At Hot Dog Queen Restaurant, the following sequence of events occurs during each minute: a With probability p, a customer arrives and waits in line. b Hot Dog Queen determines the rate s at which customers are served. If any customers are in the restaurant, then with probability s, one of the customers completes service and leaves the restaurant. It costs c(s) dollars per period to serve customers at a rate s. Each customer spends R dollars, and the customer's food costs Hot Dog Queen R - I dollars to prepare. c For each customer in line at the end of the minute, a cost of h dollars is assessed (because of customer inconvenience). d The next minute begins. Formulate a recursion that oould be used to maximize expected revenues less costs (including customer inconvenience costs) incurred during the next T minutes. Assume that initially there are no customers present