The Paris Paint Company is in the process of planning labor force requirements and production levels for the next fourquarters. The marketing department has provided production with the following forecasts of demand for Paris Paint overthe next year:Assume that there are currently 280 employees with the company. Employees are hired for at least one full quarter. Hiringcosts amount to $1,200 per employee and firing costs are $2,500 per employee. Inventory costs are $1 per gallon perquarter. It is estimated that one worker produces 1,000 gallons of paint each quarter. Assume that Paris currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of atleast 20,000 gallons. a. Determine the minimum constant workforce plan for Paris Paint and the cost of the plan. Assume that stockoouts are notallowed. b. Determine the zero inventory plan that hires and fires workers each quarter to match demand as closely as possible andthe cost of that plan. c If Paris were able to backoorder excess demand at a cost of $2 per gallon per quarter, determine a minimum constantworkforce plan that holds less inventory than the plan you found in part (a), but incurs stockoouts in quarter 2 Determinethe cost of the new plan-