Develop an aggregate production plan for a four-month period: February through May. For February and March, you should produce to exactly meet the demand forecast. 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 (zero overtime in February and March). If demand exceeds supply', then back orders occur. There are 100 workers on January 31. You are given the following unit demand forecast: February, 80,000; March, 64,000; April, 100,000; May, 40,000. Worker productivity is four units per workers hour, eight hours per day, 2 days per month. Assume zero inventory on February 1. Costs are hiring, $50 per new worker; layoff, $70 per worker laid off; inventory holding, $10 per unit per month; straight-time labor, $10 per hour; overtime $15 per hour; back order, $20 per unit per month. Find the total cost of this plan.