1. (A Forward Buying Problem) A major pharmaceutical wholesaler buys brand drugs from a manufacturer at wholesale prices and sells them to pharmacies at retail prices. It estimates that the wholesale (W) price, the retail (R) price and pharmacy sales for a blockbuster drug follow this trend: The inventory carrying cost for one unit for one month is $2. Assume enough storage capacity and zero initial inventory, how should the wholesaler take advantage of the price and demand fluctuation to maximize its profit? All decision variables: x1= units of brand drugs wholesaler buys from a manufacturer at wholesale prices in month 1 x6= units of brand drugs wholesaler buys from a manufacturer at wholesale prices in month 6 y1= units of brand drugs held in inventory from month 1 to month 2 y6= units of brand drugs held in inventory from month 6 to month 7 2. (A Transportation Problem) There are three warehouses at different cities: Detroit, Pittsburgh and Buffalo. They have 250, 130 and 235 tons of paper accordingly. There are four publishers in Boston, New York, Chicago and Indianapolis. They ordered 75,230,240 and 70 tons of paper to publish new books. The costs of transportation for one ton of paper are listed as follows: Please find the optimal plan of transportation that satisfies all orders and minimizes the total transportation cost. All decision variables: x11= number of papers (in tons) to be shipped from Detroit (DT) warehouse to Boston (BS) publisher. x34= number of papers (in tons) to be shipped from Buffalo (BF) warehouse to Indianapolis (IN) publisher