Joe Birra needs to purchase malt for his microbrewery production. His supplier charges $35 per delivery (no matter how much is delivered) and $1.20 per gallon. Joe’s annual holding cost per unit is 35% of the price per gallon. Joe uses 250 gallons of malt per week.

a. Suppose Joe orders 1000 gallons each time. What is his average inventory in gallons?

b. Suppose Joe orders 1500 gallons each time. How many orders does he place with his supplier each year?

c. How many gallons should Joe order from the supplier with each order to minimize the sum of the ordering and holding cost?

d. Suppose Joe orders 2500 gallons each time he places an order with the supplier. What is the sum of the ordering and holding costs per gallon?