4. Develop a hybrid aggregate plan with inventory, but no back orders. Also, use no undertime and no subcontracting. Also use no firing, since the company is projecting a 20% annual growth rate per year over the next several years. When demand minus opening inventory exceeds regular plus maximum overtime production, hire enough employees to meet demand, working as much overtime as possible. When demand is less than regular time production, work no overtime and add to inventory (data given above). (a) What is the workforce at the end of the last period? How many total were hired? (b) How many total units were produced using overtime? (c) What is the maximum ending inventory and when does it occur? (d) What is the total cost? Cost data Regular time labor cost per hour $10 Overtime time labor cost per hour $15 Subcontracting cost per unit (labor only) $80 Back order cost per unit per period $20 Inventory holding cost per unit per period $10 Hiring cost per employee $500 Firing cost per employee $400 Capacity data Beginning workforce 40 employees Beginning inventory O units Beginning back orders O units Production standard per unit (hours) 2 hours of labor per unit Regular time available per period (hours) 160 hours per period per employee Overtime time available per period (hours) 30 hours per period per employee Demand data Period 1 Period 5 3,920 units 2,480 units 2,200 units 3,800 units 4,340 units Period 2 Period 6 Period 3 Period 7 4,820 units Period 4 3,280 units Period 8 4,600 units