The company Enerficil Ltda is dedicated to the sale of industrial batteries. The company sold the previous year 478,400 units and expects to sell 33.3% more this year, the minimum time of delay corresponds to 25% of the delay time, considering a year of 360 days. It's known that the costs will go up 38% more than the previous year, the costs of the previous year were: order cost $370; storage cost $18 a year.

Determine:

a) What is the optimal order quantity?

b) What are the storage costs, the ordering costs, and the total cost of to hold inventory?