Clinton Manufacturing manufactures one type of pontoon boat:

Model A. The beginning inventory of the pontoon boats is 1,200 units.

Capacity is limited to the following number of boats each month: 3,000.

Demand for the pontoon boats for the next 6 months is: 1,500 in Month 1, 1,800 in Month 2, 3,000 in Month 3, 1,800 in Month 4, 1,700 in Month 5, and 1,600 in Month 6.

The production cost per unit in Months 1, 2, & 3 = $6,420. The production cost per unit in Months 4, 5, & 6 = $3,200. Holding costs are assessed on Ending Inventory each month.

The holding cost per unit in Months 1, 2, & 3 = $1,310. The holding cost per unit in Months 4, 5, & 6 = $950.

Management has specified that the ending inventory in Month 2 must be at least 408 units and that no backorders are allowed in any period.

Formulate a linear programming model to minimize total cost over the 6 months.

Decision Variables:

Objective Function:

Constraints:

Additional Work for Constraints: