$[10$ points$]$ CentraState Health is a local hospital in Freehold, NJ$.$ It is planning its inventory for the coming

year. Based on their forecast, it has been decided that they will need to order $40,000$ test packs consisting

of various rapid tests $($flu$,$ COVID etc.$)$ for its hospital for the year. A local supplier has oAered to sell them

this kit at what the procurement dept. believes are reasonable prices. The order cost for the hospital is

$$800($shipping and inspection$)$ and the unit holding cost is $$2/$unit$/$year$.$ The supplier is oAering the

following price schedule. The hospital is open $365$ days a year.

Order Size

Per unit price $$3\mathrm{.}40$ $$3\mathrm{.}20$

$0-999910,000-19,99920,000-39,00040,000+$

$$3\mathrm{.}00$

$$2\mathrm{.}80$

a$)$ How many units should the hospital order to minimize the total cost for the year?

b$)$ What is the total cost?

c$)$ What is the time between the orders?