Quarter Demand Forecast(in thousands of gallons) 1 380 630 3 220 4 160 Assume that Pairs currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of at least 20,000 gallons. a.Determine the minimum constant workforce plan for Pairs Paint and the cost of the plan. Assume that stock-outs are not allowed. b.If Pairs were able to back-order excess demand at a cost of $3 per gallon per quarter,determine a minimum constant workforce plan that holds less inventory than the plan you found in part(a), but incurs stock-outs in quarter 2.Compute the cost of the new plan. 5.(15%)A machine center in a job shop for a local fabrication company has five unprocessed jobs remaining at a particular point in time.The jobs are labeled 1,2,3,4,and 5 in the order that they entered the shop.The respective processing times and due dates are given in the table below. Job Number Processing Time(days) Due Date (days) 1 3 5 2 2 6 3 1 9 4 4 11 5 5 8 A卷总6页第3_页姓名A 卷 总 6 页 第 3 页 姓名 Quarter Demand Forecast (in thousands of gallons) 1 2 3 4 380 630 220 160 Assume that Pairs currently has 80,000 gallons of paint in inventory and would like to end the year with an inventory of at least 20,000 gallons. a. Determine the minimum constant workforce plan for Pairs Paint and the cost of the plan. Assume that stock-outs are not allowed. b. If Pairs were able to back-order excess demand at a cost of $3 per gallon per quarter, determine a minimum constant workforce plan that holds less inventory than the plan you found in part (a), but incurs stock-outs in quarter 2. Compute the cost of the new plan. 5. (15%) A machine center in a job shop for a local fabrication company has five unprocessed jobs remaining at a particular point in time. The jobs are labeled 1, 2, 3, 4, and 5 in the order that they entered the shop. The respective processing times and due dates are given in the table below. Job Number Processing Time (days) Due Date (days) 1 2 3 4 5 3 2 1 4 5 5 6 9 11 8