8. Consider a twelve-month sales and operations planning problem with the monthly demand data shown in the table below. For parts a) and b): - The inventory holding cost is $10 for each unit held at the end of a month. - Each employee makes 10 units per month. - Each hire costs $200 and each layoff (firing) costs $150. - The plan must start and end with 2 employees - The plan must start with 50 units of inventory (at the beginning of August). Month Production Inventory August September October November December January February March April May June July Demand # Hired # Fired (units) 60 80 | 60 40 100 120 60 50 TL 110 40 60 (6 pts.) a) Find the lowest total cost "level" plan (hiring is allowed only at the beginning of August and firing is allowed only at the end of July). Hiring and firing must be an integer (no fractional hiring/firing). Backordering (negative inventory) is not allowed. Fill in the table above with the number of employees hired and fired at the beginning of each month, the production and the inventory at the end of each month. # hired in August = #fired at end of July = Inventory on hand at end of July = Total cost for the plan =