Millennium Liquors is a wholesaler of sparkling wines. Its most popular product is the French Bete Noire, which is shipped directly from France. Weekly demand is $45$ cases. Millennium purchases each case for $$105,$ there is a $$350$ fixed cost for each order $($independent of the quantity ordered$),$ and its annual holding cost is $20$ percent. Assume $52$ weeks per year.

What order quantity minimizes Millennium$$s annual ordering and holding costs?

Note: Do not round intermediate calculations. Round your answer to the nearest whole number.

If Millennium chooses to order $300$ cases each time, what is the sum of its annual ordering and holding costs?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

If Millennium chooses to order $100$ cases each time, what is the sum of the ordering and holding costs incurred by each case sold?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

If Millennium is restricted to ordering in multiples of $50$ cases $($e$.$g$.,50,100,150,$ etc.$),$ how many cases should it order to minimize its annual ordering and holding costs?

Note: Do not round intermediate calculations. Round your answer to the nearest whole number.

Millennium is offered a $5$ percent discount if it purchases at least $1,000$ cases. If it decides to take advantage of this discount, what is the sum of its annual ordering and holding costs?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.