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 regular shift hour, and $140 for overtime hours. Inventory carrying cost is $4 per batch per month. There are 50 batches of inventory left over from December.

Month	Regular Time Capacity (batches)	OT Capacity (batches)	Demand (batches)
Jan.	2,880	355	3,000
Feb.	2,780	315	2,750
March	2,760	305	2,950

Use the transportation method, and assume that backlogs are not permitted. Subcontracting is not available.

What is the optimal cost? [ Select ] ["$874,320", "$902,640", "$881,230", "$911,680"]

How much unused regular time capacity is there? [ Select ] ["2880", "0", "285", "745"] batches

How much unused overtime time capacity is there? [ Select ] ["745", "8,700", "0", "965"] batches

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.

What is the optimal cost now? [ Select ] ["$874,320", "$874,200", "$868,770", "$881,440"]

How many total batches are backlogged for at least 1 month? [ Select ] ["70", "745", "0", "340"] batches