PART I: Economic Orde Quantity $($EOQ$)$

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. Assume demand rate is constant and the

delivery lead time is zero.

a$)$ Suppose Joe orders $1000$ gallons each time when he is about to run out of malt. What is the average

inventory of malt held by Joe?

b$)$ Suppose Joe orders $1500$ gallons each time when he is just about to run out of malt. What is the

average number of orders placed each year $($keep $2$ decimal place$)?$

c$)$ How many gallons should Joe order each time if he wants to minimize the total fixed ordering and

inventory holding costs each year? $($Solve EOQ$)$

d$)$ What is the total fixed ordering and inventory holding costs for the EOQ quantity for a year?

$($Calculate C$($Q$)$ for the EOQ policy$).$

e$)$ If Joe$$s supplier only accepts orders in multiples of $1000$ gallons, how many should Joe order each

time to minimize the annual total cost in managing inventories? $($Compare C$($Q$)$ for Q $=1000$ and

$2000.$ Why $1000$ and $2000?)$