PA 12-3 Joe Birra needs to purchase malt for his... Joe Birra needs to purchase
ID: 346881 • Letter: P
Question
PA 12-3 Joe Birra needs to purchase malt for his... Joe Birra needs to purchase malt for his micro-brew production. His supplier charges $25 per delivery (no matter how much is delivered) and $1.3 per gallon. Joe's annual holding cost is 25% of the price per gallon. Joe uses 250 gallons of malt per week. a. Suppose Joe orders 1000 gallons each time. What is his average inventory? 500 gallons (Round your answer to 2 decimal places.) Suppose Joe orders 1250 gallons each time. How many orders does he place with his supplier each year? 0.40 orders How many gallons should Joe order from his supplier with each order to minimize ,414 gallons c the sum of ordering and holding costs? (Round your answer to 3 decimal places.) Suppose Joe orders 2250 gallons each time he places an order with the supplier What is the sum of ordering and holding costs per gallon? 510.070 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 the annual cost of the EOQ expressed as a percentage of the annual purchase cost? 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? f gallons Joe's supplier offers a 3.00% discount if Joe is willing to purchase 8000 gallons or g. more. What would Joe's total annual cost (purchasing, ordering and holding) be if he were to take advantage of the discount?Explanation / Answer
Please find below answers to questions #e, #f and #g :
Given are following data :
Ch = Annual unit inventory holding cost = 25% of $1.3 per Gallon = $ 0.325 per gallon
Economic order quantity = EOQ = 1414 ( as calculated )
Co = Ordering cost = $25
Annual demand of malt = D = 250 gallons/ week x 52 = 13,000
Annual ordering cost = Ordering cost per delivery x Number of orders = Co x D / EOQ= $25x 13000/1414 = $229.84
Therefore, total annual cost = $229.77 + $229.84 = $459.61
Annual purchase cost = $ 1.3 per gallon x 13000 Gallons = $16900
Annual cost of EOQ as percentage of annual purchase cost
= 459.61/16900 x 100
= 2.72 %
ANNUAL COST OF EOQ AS PERCENTAGE OF ANNUAL PURCHASE COST = 2.72%
At order quantity of 1000 :
Annual Ordering cost = Co x Annual demand/1000 = $25 x 13000/1000 = $325
Annual inventory holding cost = Ch x average inventory= $0.325 x 1000/ 2 = $162.50
Total ordering and holding cost = $487.50
At order quantity of 2000 :
Annual Ordering cost = Co x Annual demand/2000 = $25 x 13000/2000 = $162.50
Annual inventory holding cost = Ch x average inventory= $0.325 x 2000/2 = $325
Total ordering and holding cost = $162.50 + $325 = $487.50
Since total cost of ordering plus holding for Order quantity 1000 < Total cost of ordering and inventory holding for order quantity 2000, the right order quantity should be Gallons 1000 Gallons
IT IS THUS CONCLUDED THAT AS FAR AS TOTAL INVENTORY COST IS CONCERNED, JOE WILL BE CONTNT WITH EITHER 1000 GALLONS OR 2000 GLLONS SINCE TOTAL ORDERING AND HOLDING COST FOR BOTH ARE SAMR.
However from the point of view of that Joe wants to economise on space to be occupied in his warehouse, Joe may order the smaller batch size i.e. 1000 Gallons
JOE SHOULD ORDER = 1000 GALLONS
Annual ordering cost = Co x D/8000 = $25 X 13000 / 8000 = $40.62
Annual inventory holding cost = Ch x 8000/ 2 =$0.325 x 8000 /2 = $1300
Unit price ( with 3 % discount ) = 97 % of $1.3 per Gallon = $1.26
Therefore , annual purchasing cost = $1.26 / Gallon x 13000 Gallons = $16380
Joe’s total annual cost = $40.62 + $1300 + $16380 = $17720.62
JOE’S TOATL ANNUAL COST = $17720.62
ANNUAL COST OF EOQ AS PERCENTAGE OF ANNUAL PURCHASE COST = 2.72%
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