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{.}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 $1,000$ gallons each time. What is his average inventory $($in

gal$)?$

$($Round your answer to $2$ decimal places.$)$

b$.$

Suppose Joe orders $1,500$ 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?

$($Round your answer to $3$ decimal places.$)$

d$.$ Suppose Joe orders $2,500$ gallons each time he places an order with the supplier.

d$.$ What is the sum of the ordering and holding costs per gallon?

$($Round your answer to $2$ decimal places.$)$

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

e$.$

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 $1,000$ gallons,

how much should Joe order to minimize ordering and holding costs per gallon?

Joe's supplier offers a $3$ percent discount if Joe is willing to purchase $8,000$ gallons

g$.$ or more. What would Joe's total annual cost $($purchasing$,$ ordering, and holding$)$ be

if he were to take advantage of the discount?

gallons

orders

gallons

per gallon

$1\%$

gallons