Joe Birra needs to purchase malt for his microbrewery production. His supplier charges $$35$ per delivery $($no matter how much is delivered$)$ and $$1\mathrm{.}25$ per gallon. Joe's annual holding cost per unit is $30$ percent of the price per gallon. Joe uses $225$ gallons of malt perweek.

a$.$ Suppose Joe orders $1,000$ gallons each time. What is his average inventory $($in gallon$)?$

Average inventory

$500$ gallons

b$.$ Suppose Joe orders $1,750$ 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

$2,413$

d$.$ Suppose Joe orders $2,500$ 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.

Costs

$\%$