TopOil, a refiner in Indiana, serves three customers near Nashville, Tennessee, and maintains consignment inventory (owned by TopOil) at each location. Currently, TopOil uses TL transportation to deliver separately to each customer. Each truck costs $800 plus $250 per stop. Thus, delivering to each customer separately costs $1,050 per truck. TopOil is considering aggregating deliveries to Nashville on a single truck. Demand at the large customer is 60 tons a year, demand at the small customer is 8 tons per year. Product cost for TopOil is $10,000 per ton, and it uses a holding cost of 25 percent. Truck capacity is 12 tons.a. What is the annual transportation and holding cost if TopOil ships a full truckload each time a customer is run-ning out of stock? How many days of inventory is carried at each customer under this policy?b. What is the optimal delivery policy to each customer if TopOil ships separately to each of them? What is the annual transportation and holding cost? How many days of inventory is carried at each customer under this policy?c. What is the optimal delivery policy to each customer if TopOil aggregates shipments to each of the three custom-ers on every truck that goes to Nashville? What is the annual transportation and holding cost? How many days of inventory are carried at each customer under this policy?d. Can you come up with a tailored policy that has lower costs than the policies in (b) or (c)? What are the costs and inventories for your suggested policy?

Amazon sells 20,000 units of consumer electronics from Samsung every month. Each unit costs $100 and Amazon has a holding cost of 20 percent. The fixed clerical and transpor- tation cost for each order Amazon places with Samsung is $4,000. What is the optimal size of the order that Amazon should place with Samsung? With the goal of reducing inven -tories, Amazon would like to reduce the size of each order it places with Samsung to 2,500 units (allowing it to get four replenishment orders every month). How much should it reduce the fixed cost per order for an order of 2,500 units to be optimal?

6. Amazon sells 10,000 Lenovo PCs every month. Each PC costs $500 and Amazon has a holding cost of 20 percent. For what fixed cost per order would an order size of 10,000 units be optimal? For what fixed cost per order would an order size of 2,500 units be optimal?