Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $$0\mathrm{.}50$ per kilogram of milk plus a $$20$ delivery fee $($the $$20$ fee is independent of the amount ordered$).$ Bruno$$s holding cost is $$0\mathrm{.}03$ per kilogram per month. He needs $9000$ kilograms of milk per month.

Suppose Bruno orders $9,000$ kilograms each time. What is his average inventory $($in kilograms$)?$

Suppose Bruno orders $7,000$ kilograms each time. How many orders does he place with his supplier each year?

Note: Round your answer to $1$ decimal place.

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

If Bruno$$s storage vessel can hold only $3,000$ kilograms of milk, what would be Bruno$$s annual ordering and holding costs if he orders this amount?

If Bruno's storage vessel can hold only $6,000$ kilograms of milk, what would be Bruno's annual ordering and holding costs if he orders this amount?

Bruno$$s supplier$$s truck can carry $20,000$ kilograms 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 $6,500$ kilograms. 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 $6,500$ kilograms.

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

Note: Round your answer to $3$ decimal places.