$1.$ A refiner in city Q serves four customers near city W and maintains consignment inventory $($owned by the refiner$)$ at each location. Currently, the refiner uses TL $($truckload$)$ transportation to deliver separately to each customer. Each truck costs $$670$ plus $$302$ per stop. The refiner is considering aggregating deliveries to city W on a single truck. The demand of the first customer is $75$ tons a year, the demand of the second customer is $30$ tons per year, and the demand of the third and fourth customers is $10$ tons per year. The product cost is $$8,000$ per ton, and it uses a holding cost of $17\%.$ The truck capacity is $20$ tons. a$.$ What is the optimal delivery policy to each customer if the refiner ships separately to each of them? What is the annual total inventory$-$related cost? b$.$ What is the optimal delivery policy to each customer if the refiner aggregates shipments to each of the four customers on every truck that goes to city W$?$ What is the annual total inventory$-$related cost? c$.$ What is the annual total inventory$-$related cost if the refiner ships a full truckload each time a customer is running out of stock? How many days of inventory are carried at each customer under this policy?