2. (50 points) A paint company is in the process of aggregate production planning for the next four quarters. The marketing department has provided the following forecasts of demand over the next four quarters for a single product family of paint: Quarter Demand forecast (in galloons) 1 380,000 2 630,000 240,000 460,000 3 4 Assume that there are currently 280 employees in the company. Each worker is paid $3000 per quarter. Employees are hired for at least one full quarter. Hiring costs is $1200 per employee and lay-off cost is $2500 per employee. Inventory holding cost is $1 per gallon per quarter. It is estimated that one worker produces 1000 gallons of paint each quarter. It costs si to produce one galloon of paint, Assume that the company currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of 250,000 gallons. Assume that it is a competitive market and customers are not willing to wait for backorders, hence backordering is not allowed. Assume that the manufacturer charges the inventory holding cost based on average inventory level, Develop the constant work force plan for the company by filling in the table on the next page. (Show your work, either by drawing a diagram or by using mathematical operations. If there are similar computations, it is enough to show only one sample computation.)