An Eastern Pennsylvania chain of dental clinics orders $3,000$ cases of bibs per year. There is a $$50$ charge for placing an order and the chain has a $$5\mathrm{.}00$ annual cost for holding each case of bibs. How much should they order each time to minimize total annual costs?

Eo a carry toral annual

A$)100$ cases

B$)174$ cases

C$)200$ cases

D$)245$ cases

E$)548$ cases