Joe Birra needs to purchase malt for his microbrewery production. His supplier charges $$30$ per delivery $($no matter how much is

delivered$)$ and $$1\mathrm{.}05$ per gallon. Joe's annual holding cost per unit is $25$ percent of the price per gallon. Joe uses $225$ gallons of malt

per week.

a$.$ Suppose Joe orders $750$ gallons each time. What is his average inventory $($in gallon$)?$

Average inventory

gallons

b$.$ Suppose Joe orders $1,500$ gallons each time. How many orders does he place with his supplier each year?

Note: Round your answer to $2$ decimal places.

Number of orders

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

Number of gallons

d$.$ Suppose Joe orders $2,250$ gallons each time he places an order with the supplier. What is the sum of the ordering and holding

costs per gallon?

Note: Round your answer to $3$ decimal places.

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?

Note: Round your answer to $2$ decimal places.