A cake factory can produce cakes at the rate of $500$ per day. The factory supplies its cakes to local grocery stores at a rate of $250$ per day. The cost to prepare the equipment for producing the cakes is $$20.$ Annual holding costs are $$2$ per cake. Assume that the factory operates $250$ days a year.

Refer to the information above. What is the optimal EPQ?

A$)1389$

B$)1425\mathrm{.}68$

C$)1250\mathrm{.}27$

D$)1000$

E$)1581\mathrm{.}14$