1. The Metropolitan Bus Company (MBC) purchases diesel fuel from American Petroleum Supply. In addition to the fuel cost, American Petroleum Supply charges MBC $250 per order to cover the expenses of delivering and transferring the fuel to MBC's storage tanks. The replenishment lead time for a new shipment from American Petroleum is assumed to be 0; the cost of holding a gallon of fuel in the storage tanks is $0.04 per month; and monthly fuel usage is 15,000 gallons. MBC buses operate 300 days a year. What is the optimal order quantity for MBC? How much is the cycle inventory? How much is the number of orders per year? How much is the total annual ordering and holding cost? How many days are the average flow time? If the order quantity is changed to 10,000, please explain the total annual ordering and holding cost will increase or decrease. 2. (Production Lot Size model) Beauty Bar Soap is produced on a production line that has an annual capacity of 50,000 cases. The annual demand is estimated at 28,000 cases, with the demand rate essentially constant throughout the year. The cleaning, preparation, and setup of the production line cost approximately $145. The manufacturing cost per case is $5.50, and the annual holding cost is figured at a 24% rate. Other relevant data include 250 working days per year. How much is the optimal production quantity? How much is the percentage of the machines being used (machine utilization)? How much will be the annual holding cost? And annual set up cost? 3. Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westside's generator production operation, which is operated at a constant rate, will require 40000 components per quarter throughout the year. Assume that the ordering costs are $150 per order, the unit cost is $2.40 per component, and annual holding costs are 20% of the value of the inventory. Westside has 250 working days per year. What is the optimal order quantity for Westside Auto? How much is the cycle inventory? how much would be the number of orders per year? How much is the total annual ordering and holding cost? How many days are the average flow time? 4. Nick's Camera Shop carries Zodiac instant print film. The film normally costs Nick $3.50 per roll, and he sells it for $5.50. Just assume Zodiac film has no shelf life. Nick's average sales are 21 rolls per week. His annual inventory holding cost rate is 25% and it costs Nick $20 to place an order with Zodiac. If Zodiac offers a 7% discount on orders of 400 rolls or more, a 10% discount for 900 rolls or more, and a 18% discount for 2000 rolls or more, determine Nick's optimal order quantity. Suppose The shop opens 280 days annually.