Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $0.50 per kg of milk plus a $20 delivery fee (the $20 fee is independent of the amount ordered). Bruno's holding cost is $0.03 per kg per month. He needs 9000 kg of milk per month.

a. Suppose Bruno orders 9000 kg each time. What is his average inventory (in kilograms)?

b. Suppose Bruno orders 7000 kg each time. How many orders does he place with his supplier each year?

c. How many kg should Bruno order from his supplier with each order to minimize the sum of the ordering and holding costs?

d. If Bruno's storage vessel can hold only 3000 kg of milk. what would be Bruno's annual ordering and holding costs?

e. If Bruno's storage vessel can hold only 6000 kg of milk. what would be Bruno's annual ordering and holding costs?

f. Bruno's supplier's truck can carry 20.000 kg of milk. The supplier does not want to deliver to more than three customers with each truck. Thus, the supplier requires a minimum order quantity of 6500 kg. If Bruno orders the minimum amount, what would be the sum of his annual ordering and holding costs? Assume he has a storage vessel large enough to hold 6500 kg.

g. Bruno's supplier offers a 5 percent discount when a customer orders a full truck, which is 20,000 kg. Assume Bruno can store that quantity and the product will not spoil. If Bruno orders a full truck, what would be the inventory holding and ordering cost incurred per kilogram of milk?