Var Names x1 x2 x3 x4 x5 x6 y1 y2 y4 y5 Operator Value RHS Var Value Objective Fn subject to Constraint 1 Constraint 2 Constraint 3 Constraint 4 Constraint 5 Constraint 6 Constraint 7 max 20000000 = 30000000 45000000 60000000 75000000 = 95000000 0 (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: + W price ($/unit) R price ($/unit) Demand Month 1 40 2 3 4 5 6 45 55 60 65 70 80 90 110 120 130 140 20 million 30 million 45 million 60 million 75 million 95 million (in units) 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? (10 pts) + 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: New York Chicago From To Boston (BS) (NY) (CH) Indianapolis (IN) Detroit (DT) 15 20 16 21 Pittsburgh 25 13 5 11 (PT) Buffalo (BF) 15 15 7 17 Please find the optimal plan of transportation that satisfies all orders and minimizes the total transportation cost (10 pts). The optimal 3. (Sensitivity Analysis) Consider the following linear programming problem: Maximize 1x + 2x2 Subject to x1 + x2 12 x 8 x26 X1, X2 0 Please get the answer and sensitivity reports using Excel. a. What is the optimal solution and the optimal objective function value? (2pt) b. If the objective function was changed to maximize 1x +5x2 would the optimal solution of x = 6 and x2 = 6 change? If yes then what is the new optimal solution point? (2pt) c. If the objective function was changed to maximize 1x +5x2 would the optimal objective function value of 18 change? If yes then what is the new optimal objective function value? (2pt) d. The shadow price of the original problem is 1 for constraint 1 so if the RHS current value of 12 is increased by one to 13 what is the effect if any on the current optimal objective function value of 18? (2pt) e. The shadow price of the original problem is 1 for constraint 1 so if the RHS current value of 12 is increased by 0.5 to 13.5 what is the effect if any on the current optimal objective function value of 18? (2pt) f. The shadow price of the original problem is 0 for constraint 2 so if the RHS current value of 8 is increased by one to 9 what is the effect if any on the current optimal objective function value of 18? (2pt) g. Which constraint of the original problem is binding, constraint 1 or 2 and why? (2pt)