Jessica Lyell of Action Video Games has received a contract to produce and man- ufacture two new games for the Wii platform. The first, Downhill Adventure, allows simulating skiing down a variety of slopes against a friend or the clock using a pair of ski pole controllers. The second game, En Guarde, allows players to engage in swordplay using a sword-like controller. Action Video Games wants to plan its production schedule for the next three months for these two games. GAME BEGINNING INVENTORY PRODUCTION PRODUCTION POUNDS OF PLASTIC PER GAME INVENTORY COST PER GAME PER HOUR) PER GAME Downhill Adventure 500 13 15 $18 $1.2 En Garde 750 2 20 $14 SCHEDULE PLASTIC AVAILABLE (POUNDS) TIME AVAILABLE (HOURS) MONTHLY DEMAND MONTHLY DEMAND DOWNHILL EN GUARDE ADVENTURE January 20,000 500 2,200 4,500 February 20,000 500 3,500 6,000 March 20,000 500 2,500 5,000 a. Develop a linear programming model that would tell Jessica how many of each game to produce and inventory level each month to minimize the total cost. Clearly define all variables used. Inventory cost will be levied on any items in inventory at the end of each month, after demand for the month has been sat- isfied. The company wants to end the three-month period with 1,500 Downhill Adventure games and 1,000 En Guarde games in inventory.
b. Use Solver to find the optimal solution to the linear program from part a.