Given the projected demands for the next six months, prepare an aggregate plan that uses inventory, regular time and overtime, and backorders. The plan must wind up with no units in ending inventory in Period 6. Regular time capacity is 150 units per month. Overtime capacity is 20 units per month. Overtime cost is $30 per unit, backorder cost is $20 per unit, inventory holding cost is $5 per unit, regular time cost of $20 per unit, and beginning inventory is zero. Month Forecast 1 180 2 170 3 140 4 150 5 130 6 150 How should overtime capacity be utilized? (In what period, and how many units) What are the total regular time costs? What are the total backorder costs? What is the total cost for this plan?