Ergonomics Incorporated sells ergonomically designed office chairs. The company has the following information:

Average demand $=31$ units per day

Average lead time $=45$ days

Item unit cost $=$$$65$ for orders of less than $350$ units

Item unit cost $=$$$63$ for orders of $350$ units or more

Ordering cost $=$$$40$

Inventory carrying cost $=20\%$

The business year is $250$ days.

a$.$ How many chairs should the firm order each time? Assume there is no uncertainty at all about the demand or the lead time.

b$.$ What will the firm's average inventory be under each alternative?

c$.$ What will be the annual ordering and holding costs for each alternative?