Joe Birra needs to purchase malt for his microbrewery production. His supplier charges $35per delivery (no matter how much is delivered) and $1.20 per gallon. Joe’s annual holdingcost per unit is 35 percent 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 gal)?b. Suppose Joe orders 1500 gallons each time. How many orders does he place with hissupplier each year?c. How many gallons should Joe order from his supplier with each order to minimize thesum of the ordering and holding costs?d. Suppose Joe orders 2500 gallons each time he places an order with the supplier. Whatis the sum of the ordering and holding costs per gallon?e. Suppose Joe orders the quantity from part (C) that minimizes the sum of the orderingand holding costs each time he places an order with the supplier. What is the annualcost of the EOQ expressed as a percentage of the annual purchase cost?f. If Joe’s supplier only accepts orders that are an integer multiple of 1000 gallons, howmuch should Joe order to minimize ordering and holding costs per gallon?g. Joe’s supplier offers a 3 percent discount if Joe is willing to purchase 8000 gallons ormore. What would Joe’s total annual cost (purchasing, ordering, and holding) be if hewere to take advantage of the discount?

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 percent 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 gal)?
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 his supplier with each order to minimize the
sum of the ordering and holding costs?
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?
e. Suppose Joe orders the quantity from part (C) that minimizes the sum of the ordering
and holding costs each time he places an order with the supplier. What is the annual
cost of the EOQ expressed as a percentage of the annual purchase cost?
f. If Joe’s supplier only accepts orders that are an integer multiple of 1000 gallons, how
much should Joe order to minimize ordering and holding costs per gallon?
g. Joe’s supplier offers a 3 percent discount if Joe is willing to purchase 8000 gallons or
more. What would Joe’s total annual cost (purchasing, ordering, and holding) be if he
were to take advantage of the discount?