If a CD manufacturing company produces a variety of different CDs for computers. The CDs are produced at a rate of 200,000 per day and shipped out at a rate of 20,000 per day. The CDs are produced in batches. Each CD cost the company 20 cents, and the holding costs are based on a 20 percent annual interest rate. Shortages are not permitted. Each production run of a CD type requires re-calibration of the equipment. The company estimates that this calibration costs $180. (a) Find the optimal sizes of each production run and the cycle time (b)What Fraction of the time is the company producing CDs and the machine is idle? (c) Suppose the storage will have a maximum inventory of 230,000 CDs. If 50 CDs are boxed in a 5" x 6" x6" case with base 6" x 6" what should be the minimum height of a storage room with 12.5-ft square (i.e. 12.5' x 12.5') floor to accommodate the CD cases? Show your work