1) (30pts) A manager is making production planning for the next 6 months. Demand forecasts in aggregate units are 80, 90, 120, 50, 60, 150 for months 1 to 6. The company has a workforce of 100 and it is not possible to change the number of workers by hiring or firing. Each worker is capable of producing 0.03 aggregate units in one workday. The available workdays are given as 20, 17, 22, 21, 19, 18 for months 1 to 6 respectively. Unit production cost is 8 liras per aggregate unit. It is not possible to manufacture during overtime but there is a possibility of subcontracting at a cost of 12 liras per aggregate unit. Inventory holding cost is 5 liras per unit per month. Backordering cost is 7 liras per unit per month. Beginning inventory is 30 aggregate units (hence backorders at the beginning of first month are zero). Ending inventory and backorders at the end of sixth month should be planned to be zero. Undertime costs are negligible. The maximum amount of subcontracted items are 50 aggregate units per month. Formulate the aggregate planning problem as an LP. State all variables and costs explicitly While answering this question (and the other questions below) make use of the following decision variables Pi. P.. P…. Production quantities in months 1, 2, 3, .. S, S, S,… Subcontracted quantities in months 1, 2, 3, Ii, I, Is,.. Inventory-on-hand at the end of months 1, 2, 3, B, B, B,… Backorders at the end of months 1, 2, 3,