Johnson's Juice sells bottles of "Keep Me Awake During Class" fruit juice to college students. Annual demand is $87,000$ bottles. The company uses an annual holding cost percentage of $15\mathrm{.}5\%,$

it its setup cost is $$46$ per order. The current price per bottle from the supplier is $$0\mathrm{.}85,$ and Johnson's Juice resells it to customers for $$2\mathrm{.}00$ each. However, the supplier has notified Johnson's

Juice that starting next week, the purchase price will rise to $$1\mathrm{.}13$ due to tariffs imposed by the government. Johnson's inventory of bottles is about to be depleted. $($Assume that the bottles are

so full of chemicals that the drinks never expire.$)$

a$.$ Which inventory model fits the best to this problem?

A$.$ Incremental quantity discounts model

B$.$ All$-$units quantity discounts model

C$.$ Lumpy demand model

D$.$ One$-$time sale model

b$.$ Johnson's Juice should purchase

bottles in the next order $($round your response to the nearest integer$).$