As the production manager of the Neptune Boat Corporation, youmust determine how many units of the Model 4W speedboat to produceover the next four quarters. The company has a starting inventoryof 75 units, and demand is 125 units in quarter 1, 100 units inquarter 2, 40 units in quarter 3, and 20 units in quarter 4.Production capacity is limited to 70 units in quarter 1, 90 unitsin quarter 2, 50 units in quarter 3, and 60 units in quarter 4. Theinventory cost during quarters 1 and 2 is $200 per unit perquarter, and $300 per unit per quarter during quarters 3 and 4.Production costs for the first quarter are $8,000 per unit, andthese costs increase by 10% per quarter due to increasing labor andmaterial costs. Neptune’s senior management has indicated that theending inventory for quarter 4 must be at least 30 units. Develop alinear programming model that Neptune can use to determine theoptimal production schedule that will minimize the total cost ofmeeting demand for the Model 4W speedboat in each quarter, subjectto the capacity and inventory constraints. You do not need to solvethe LP.
