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 $$120,$ there is a $$300$ fixed cost for each order $($independent of the quantity ordered$),$ and its annual holding cost is $25$ percent.

$($Do not round intermediate calculations. Round your answer to the nearest whole number.$)$

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

$($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

b$.$ ordering and holding costs?

$($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

cHoMiling cuss chouses boy eder to esseg each tme., What is the sum of the ordering and

$($Do not round intermediate calculations. Round your answer to the nearest whole

number.$)$

$($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

e$.$ to take advantage of this discount, what is the sum of its annual ordering and holding