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

$$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$\text{'}$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$\text{'}$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 kg of milk?