2. Consider the following Sales and Operations Planning problem: The forecasted demand for the next five months is 550, 430, 800, 750, 330 units. Each unit of product takes a worker 2 hours to process. Each worker can work for 160 hours a month for regular time and at most 30 hours of overtime. The plant currently employs 8 workers. Demand has to be satisfied in full. Hiring one worker costs $1000 and layoff costs $500. Inventory can be held at $2/unit/month. The regular wage is $10/hour and overtime wage is $15/hour. Workers are only paid for the time they worked. Assume that workers can be noninteger numbers. (1) Find a chase strategy and a level strategy without using overtime or inventory. Compute the total cost. (2) Find an optimal strategy if overtime is allowed. Compute the total cost. (3) Find an optimal strategy if inventory is allowed. Compute the total cost. (4) Find an optimal strategy if both overtime and inventory are allowed. Compute the total cost.