supply chain management problem urgent help needed

2. The manager of Hariboru Toy Cars uses overtime, inventory and subcontracting to absorb fluctuations in demand. An aggregate production plan is devised annually and updated quarterly. Forecasted demands and available capacities in aggregate units (average toy car) for the next four quarters are given below. Quarter, t 1 Demand Forecast 1400 Regular Capacity 1300 Overtime Capacity 200 Subcontract Capacity 500 2 2500 1300 200 500 3 1400 1300 200 500 4 2400 1300 200 500 Demand must be satisfied in the period it occurs. That is, backorders are not allowed. The regular production cost is 20 TL/unit, the overtime production cost is 25 TL/unit, and the subcontracting cost is 28 TL/unit, the inventory holding cost is 3 TL/unit/period. Hariboru produces three types of cars where the second one is accepted as the "average toy car". It is known that value of the first car is haft of the value of the average car. On the other hand, value of the third car doubles value of the average car. Hariboru has 100 cars of first type, 150 cars of second type and 50 cars of third type on hand at the beginning of the planning horizon. The manager wants to determine the minimum-cost aggregate production plan over the planning horizon. a. Formulate the problem as a transportation problem. b. Find the minimum-cost solution for this problem using the transportation model in (a). c. Now suppose that backorders are allowed at 2 TL/unit/quarter. Modify the transportation problem formulation in part (a) and find the minimum-cost aggregate production plan. d. Which plan turned out to be better in terms of total cost? e. Draw the cumulative demand and cumulative supply (regular production + overtime + subcontracts) curves over time separately for the two cases: w/ backorders and w/o backorders. Observe the two graphs in terms of inventory and backorder accumulation thru time