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Problem 3: Standard Pump recently won a $14 million contract with the U.S. Navy to supply 2000 custom- designed submersible pumps over the next four months. The contract calls for the delivery of 200 pumps at the end of May, 600 pumps at the end of June, 600 pumps at the end of July, and 600 pumps at the end of August. Standard's production capacity is 500 pumps in May, 400 pumps in June, 800 pumps in July, and 500 pumps in August. Following relationship holds between beginning and ending inventory of each month. (Beginning Inventory) + (Current Production) - (This Month's Demand) (Ending Inventory) = Management would like to develop a production schedule that will keep monthly ending inventories low (ideally 0) while at the same time minimizing the fluctuations in production level (ideally level production strategy with same number of pumps produced each month). Assuming the production fluctuation and inventory goals are of equal importance, develop and solve an optimization model to determine the best production schedule for next 4 months. List clearly: 1) How many pumps should be produced in May, June, July and August 2) Value of optimization function. What this number tells you