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: W price ($/unit) R price ($/unit) Demand (in units) 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 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) + + Forward Buying Decision Variables x (1-6) = Months, y (1-6) = Inventory Carrying cost Levels Operator Maximize Profit - 40x1 - 45x2 - 55x3 - 60x4 - 65x5 - - 70x6-2y1-2y3 2y4 - 2y5 2y6 Subject to Constraint 1 y0+x1-y1 Constraint 2 y1 + x2 - y2 Constraint 3 y2+x3-y3 Constraint 4 y3+x4-y4 Constraint 5 y4+x5-y5 Constraint 6 y5+x6-y6 Constraint 7 Resources = 20,000,000 = 30,000,000 = || 45,000,000 = 60,000,000 = || 75,000,000 = 95,000,000 >= 0 Non-negativity Var Names x1 x2 x3 x4 x5 x6 y1 y2 y3 y4 Var Value Objective Fn 40 45 45 55 60 60 subject to Constraint 1 Constraint 2 Constraint 3 Constraint 4 Constraint 5 Constraint 6 HOOOOO 1 0 0 0 0 0 OHOOOO 0 1 0 0 0 0 OOHO00 1 OOO100 65 70 2 2 2 y5 2 2 Operator Value RHS 2 max 0 0 0 0 0 1 OOOOO 0 -1 0 0 0 0 0 1 -1 0 0 1 1 -1 0 0 1 1 1 -1 OOOO 0 0 = 20000000 0 0 = 30000000 0 0 = 45000000 0 0 = 60000000 0 1 1 1 1 -1 0 = 75000000 0 1 1 1 1 1 1 -1 = 95000000