Consider a twelve-month sales and operations planning problem with the monthly demand data shown in the table below. - The inventory holding cost is $20 for each unit held at the end of a month. - Each employee makes 5 units per month. - Each hire costs $600 and each layoff (firing) costs $400. - The plan must start and end with 8 employees. - The plan must start with 50 units of inventory (at the beginning of August). - The plan must end with at least 50 units of inventory at the end of July. Find the lowest cost S&OP plan where all hiring and firing must be in integers (no fractions). Backordering (negative inventory) is not allowed. a) Report the total cost of your plan. b) Fill in the table below to show the number of employees hired and fired at the beginning of each month, the production and the inventory at the end of each month. a) Total cost for the plan = b) Fill in the table: Month # Hired # Fired Production Inventory (50) August September October November December January February March April May Demand (units) 60 80 60 40 100 120 60 50 60 110 40 60 June July