Binford Tools manufactures garden tools. It uses inventory, overtime, and subcontracting to absorb demand fluctuations. Expected demand, regular and overtime production capacity, and subcontracting capacity are provided in the following table for the next four quarters for its basic line of steel garden tools:

Quarter Demand Regular Capacity Overtime Capacity Subcontracting Capacity 1 9,000 9,000 1,000 3,000 2 12,000 10,000 1,500 3,000 3 16,000 12,000 2,000 3,000 4 19,000 12,000 2,000 3,000 The regular production cost per unit is $20, the overtime cost per unit is $25, the cost to subcontract a unit is $27, and the inventory carrying cost is $2 per unit. The company has 300 units in inventory at the beginning of the year.

Determine the optimal production schedule for the four quarters to minimize total costs.