An automobile manufacturer needs to plan its production for the next 12 months. Demands for the next 12 months are forecasted to be 940, 790, 360, 720, 270, 130, 160, 300, 990, 290, 280, and 790. Other relevant information is as follows: Workers are paid $5,000 per month; It costs $500 to hold a car in inventory for a month. The holding cost is based on each months ending inventory; It costs $4,000 to hire a worker; while it costs $6,000 to fire a worker. Workers are hired and fired at the beginning of each month; Each worker can make up to eight cars per month; At the beginning of month 1, there are 500 cars in inventory and 60 workers. The manufacturer wants to minimize the total inventory and staffing cost of meeting demands for cars in the next 12 months.

a)Define the decision variables and write down the detailed mathematical formulation of the automobile manufacturers optimization problem.

b)Solve the optimization problem by Excel Solver. Write down the manufacturers detailed optimal production and staffing plan for the next 12 months.