2. A manufactured product has a constant demand rate of 10000 units per year. The machine used to manufacture this item has a production rate of 140000 units per year, therefore the product will be produced in batches rather than continuously. Because the units are produced sequentially, the rate of addition to inventory is finite. The machine setup cost is $400 and unit variable production cost is $25. No shortages are to be allowed. a) If the annual inventory carrying cost rate is 0.20 , what is the economic production lot size? b) If the manufacturer uses a lot size of 4000 , what inventory carrying cost rate is s/he implicitly assuming? That is, for what inventory carrying cost rate would 4000 be optimal