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https//www.mathxl.com/Student/PlayerHomework.aspx?homeworkld-4641115238questionld-7&flushed-true8icld-48287078centerwin-yes; MQM 227-Operations Management- Spring 2018 Austin Karpinski 3/5/18 10:07 PM Homework: Chapter 12: Homework Save Score: 0 of 1 pt HW Score: 80%, 8 of 10 pts Problem 12.25 Question Help * tOE Rocky Mountain Tire Center sels 7000 go cart tires per year The on ring cost rear der s s and me na din r st is 4 % at the chase pnce ofthe res per year The p rchase price is $20 er tire it e er than00 tire are or red 51 per tire it o or more, but fewer than 5,000, tires are ordered, and $13 per tire if 5,000 or more tires are ordered. a) How many tires should Rocky lountain order eacn time t places aorder? Rocky Mountain's optimal order quantty is units fenter your response as e whole number. Enter your answer in the answer box and then click Check Answer Clear Al Final Check 10:07 PMExplanation / Answer
Annual demand (D) = 7000 tires
Ordering cost (S) = $40
Order quantity price Holding cost (40% of price)
Fewer than 200 $20 $8
200-5000 $16 $6.4
More than 5000 $13 $5.2
First we have to find the minimum point for each price starting with the lowest price until a minimum feasible point is located.
Minimum point for price of $13 = sqrt of (2DS /H) = sqrt of [(2 x 7000 x 40)/5.2] = 328 tires. As an order quantity of 328 tires will cost $16 instead of $13, it is not a feasible point.
Minimum point for price of $16 = sqrt of (2DS /H) = sqrt of [(2 x 7000 x 40)/6.4] = 296 tires. Since an order quantity of 296 tires will cost $161 it is a feasible point
With order quantity (Q) = 296 units,
Total cost = Ordering cost + Holding cost + purchase cost
= [(D/Q) S] + [(Q/2)H] + (price x D)
= [(7000/296)40] + [(296/2)6.4] + (16 x 7000)
= $945.95 + $947.2 + $112000
= $113893. 15
Minimum order quantity needed to obtain a price of $13 is 5000 units. So with order quantity(Q) = 5000 units,
Total cost = Ordering cost + Holding cost + purchase cost
= [(D/Q) S] + [(Q /2)H + (price x D)
= [(7000/5000)40] + [(5000/2)5.2] + (13 x 7000)
= $56 + $13000 + $91000
= $104056
a) Since the total cost when ordering 5000 per order is less than the total cost of ordering 296 per order, Rocky Mountain tire center's optimal order size is 5000 units.
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