As the production manager of the Neptune Boat Corporation, you must determine how many units of the Model 3Z boat to produce over the next four quarters. The company has a starting inventory of 100 units, and demand is 2,000 units in quarter 1, 4,000 units in quarter 2, 3,000 units in quarter 3, and 1,500 units in quarter 4. Production capacity is limited to 4,000 units in quarter 1, 3,000 units in quarter 2, 2,000 units in quarter 3, and 4,000 units in quarter 4. The inventory cost during quarters 1 and 2 is $250 per unit per quarter, and $300 per unit per quarter during quarters 3 and 4. Production costs for the first quarter are $10,000 per unit, and these costs increase by 10% per quarter due to increasing labor and material costs. Neptune’s senior management has indicated that the ending inventory for quarter 4 must be at least 500 units.
Develop a linear programming model that can be used to determine the optimal production schedule that will minimize the total cost of meeting demand in each quarter, subject to the capacity and ending inventory constraints. You do not need to solve the LP.