Joe Birra needs to purchase malt for his micro-brew production. His supplier cha
ID: 369502 • Letter: J
Question
Joe Birra needs to purchase malt for his micro-brew production. His supplier charges $35 per delivery (no matter how much is delivered) and $1 05 per gallon. Joe's annual holding cost is 25% 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? gallons Round your answer to 2 decimal places,) Suppose Joe orders 2000 gallons each time. How many orders does he place with orders his supplier each year? How many gallons should Joe order from his supplier with each order to minimize (Round your answer to 3 decimal places.) What is the sum of ordering and holding costs per galion? (Round your answer to 2 decimal places.) gallons the sum of ordering and holding costs? d Suppose Joe orders 3000 gallons each time he places an order with the supplier. per gallon Suppose Joe orders the quantity from part (c) that minimizes the sum of the e. 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 1,000 gallons, gallons how much should Joe order to minimize ordering and holding costs per gallon? Joe's supplier offers a 3.00% discount if Joe is willing to purchase B000 gallon he were to take advantage of the discount? g.more. What would Joe's total annual cost (purchasing, ordering and holding) be ifExplanation / Answer
Answer to question a :
Annual demand of malt = 225 Gallons/ week x 52 weeks = 11700 Gallons
Order quantity = 750 Gallons each time
Average inventory = Order Quantity / 2 = 750/ 2 = 375 Gallons
Answer to question b :
New order quantity = 2000 Gallons
Number of orders in a year = Annual demand / Order quantity = 11700/ 2000 = 5.85
Answer to question c:
We have to establish Economic Order Quantity ( EOQ ) as per relevant model to minimize ordering and holding cost
Accordingly,
EOQ = Square root ( 2 x Co x D / Ch)
D = Annual demand = 11700 Gallons
Co = Ordering cost = $35
Ch = Annual unit Holding cost = 25% of $1.05 = $ 0.2625
Thus ,
EOQ = Square root ( 2 x 35 x 11700 / 0.2625)
= 1766.352
JOE SHOULD ORDER 1766.352 GALLONS TO MINIMIZE SUM OF ORDERING AND HOLDING COST
Answer to question d :
When order quantity = 3000 Gallons
Annual ordering cost = Ordering cost x Number of orders
= Ordering cost x Annual demand / Order quantity
= 35 x 11700/3000
= $136.5
Annual holding cost = Annual unit holding cost x Average inventory
= $0.2625 x 3000/ 2
= $393.75
Thus, sum of ordering and holding cost for order qty of 3000 = $136.5 + $393.75 = $530.25
Thus, Sum of ordering and holding cost per Gallon = $530.25/ 3000 = $ 0.1765 ( $0.18 rounded to 2 decimal places )
SUM OF ORDERING AND HOLDING COST PER GALLON = $ 0.18
Answer to question e :
For order quantity = EOQ = 1766.352 Gallons,
Annual ordering cost = Ordering cost x Number of orders
= Ordering cost x Annual demand / Order quantity
= 35 x 11700/1766.352
= $ 231.83
Annual holding cost = Annual unit holding cost x Average inventory
= $0.2625 x 1766.352 / 2
= $ 231.83
Thus, sum of ordering and holding cost for order qty of 3000 = $231.83 + $231.83 = $ 463.66
Annual purchase cost = $1.05 / Gallon x 11700 Gallons = $12285
Thus,
Annual cost of EOQ as percentage of Annual purchase cost = 463.66/12285 x 100 = 3.774 %
ANNUAL COST OF EOQ AS PERCENTAGE OF ANNUAL PURCHASE COST = 3.774%
Answer to question f :
If order quantity should be such that it minimizes total ordering and holding cost and yet is multiple of 1000, then the order quantity should be multiple of 1000 and should be the nearest one to theoretical EOQ of 1766.352 .
Thus order quantity should be = 2000
Answer to question g :
With 3% price discount , the discounted unit price = 97% of $1.05 = $1.0185
Thus , Unit annual holding cost = 25% of $1.0185 = $ 0.2546
New order quantity = 8000
Thus,
Annual ordering cost
= Ordering cost x Number of annual orders
= Ordering cost x Annual demand / Order Quantity
= 35 x 11700 / 8000
= $51.875
Annual holding cost
= Annual unit holding cost x Average inventory
=0.2546 x 8000/2
= $1018.40
Annual purchasing cost = $1.0185/ unit x 11700 units = $11916.45
Thus Joe’s total cost
= $11916.45 + $1018.40 + $51.875
= $12986.725
JOE’S TOTAL ANNUAL COST = $12986.725
JOE SHOULD ORDER 1766.352 GALLONS TO MINIMIZE SUM OF ORDERING AND HOLDING COST
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