Demand for widgets is normally distributed with a daily average of $30$ units, standard deviation of $4$ units. Lead time from the supplier is $3$ days. Order costs are $$50$ per order. Holding cost is $$1$ per unit per year.

a$.)$ What is the optimal order size?

b$.)$ What ROP should be used to maintain a $98\%$ service level?

c$.)$ What would the total cost of the system you calculated in parts a$.$ and b$.$ be$?$

d$.)$ When would a fixed period system be preferable to a fixed quantity system?