A manufacturer wants to develop a production plan for the month of February through June. The forecasted demand for those months are 2500, 3700, 3900, 5000, and 2000 units, respectively. The regular-time production capacity in February and March are 3000 units and 2500 units, respectively. The overtime production capacity in February and March are 600 units and 500 units, respectively. The regular production cost is $30 per unit and the overtime production cost is $45 per unit. The cost of holding a unit in inventory is $0.55 per month. The monthly cost of holding inventory is calculated based on the inventory level at the end of the month. The inventory level at the beginning of February is estimated to be 140 units. The manufacture wants to fully satisfy monthly demands. Furthermore, the manufacturer also wants to have at least 50 units in inventory at the end of each month.

To simplify, we will only look at the production decision in February and March. We must help the manufacturer to find the most economical production decision without SOLVER. What is the best production decision for the manufacturer? Explain briefly. What is the total production and inventory cost for February and March?