You are to plan production for a four-month period: February through May. For February and March, you should produce to the exact demand forecast. During February and March, you will follow a matching strategy and hire and layoff the works as required. For April and May, you should use overtime and inventory with a stable workforce. Stable means that the number of workers needed for March will be held constant through May. However, government constraints put a maximum of 5,000 hours of overtime labor per month in April and May. There is no overtime allowed in February and March. If demand exceeds supply, then backorders occur. If there is excess capacity in May, the workers are paid but there is no work performed hence there are no extra units produced in May. There are 100 workers on January 31. You are given the following demand forecast

February - 80,000

March - 64,000

April - 100,000

May - 40,000

Productivity is four units per worker hour. Each worker works eight hours per day, 20 days per month. Assume zero inventory on February 1. There is to be no inventory at the end of May. Hiring costs are $50 per worker, while layoff costs are $70 per worker. The inventory holding cost is $10 per unit per month based on the number of units in inventory at the end of the month. Straight time labor is $10 per hour and overtime is 150% of the straight time labor rate. Backorder costs are $20 per unit per month.

Find the total cost of this plan.