Consider the following inventory problem. You are running a company that sells some large product (lets assume you sell trucks), and predictions tell you the quantity of sales to expect over the next n months. Let d i denote the number of sales you expect in month i. Well assume that all sales happen at the beginning of the month, and trucks that are not sold are stored until the beginning of the next month. You can store at most S trucks, and it costs C to store a single truck for a month. You receive shipments of trucks by placing orders for them, and there is a xed ordering fee of K each time you place an order (regardless of the number of trucks you order). You start out with no trucks. The problem is to design an algorithm that decides how to place orders so that you satisfy all the demands {d i }, and minimize the costs. In summary: There are two parts to the cost: (1) storageit costs C for every truck on hand that is not needed that month; (2) ordering feesit costs K for every order placed. In each month you need enough trucks to satisfy the demand d i , but the number left over after satisfying the demand for the month should not exceed the inventory limit S. Give an algorithm that solves this problem in time that is polynomial in n and S.