A foundry produces cast-iron ingots. While preparing a three month aggregate plan, the operations manager uncovered the following information: The cost of producing a batch of ingots is $100 per batch produced on regular shift hours, and $140 for batches produced on overtime hours. Inventory carrying cost is $4 per batch per month. There are 50 batches of inventory left over from December. Month OT Capacity (batches) Demand (batches) Regular Time Capacity (batches) 2.880 2,780 Jan. 355 3,000 2.750 Feb. March 315 305 2,760 2.950 Use the transportation method, and assume that backlogs are not permitted. Subcontracting is not available. a. What is the optimal cost? Select] v b. How much unused regular time capacity is there? [Select] batches c. How much unused overtime time capacity is there? [Select] batches d. What if 45 units are required to be held into the next planning period (i.e. April), what would the total cost be? Select] Suppose that the foundry discovers that customers are willing to wait for their orders, and there is no cost to the foundry. In other words, backlogging is permitted at $0 cost, and the 45 units for April mentioned above are no longer needed e. What is the optimal cost now? [Select] f. How many total batches are backlogged for at least 1 month? Select] batches