Rocky Mountain Tire Center sells 14,000 go-cart tires per year. The ordering cos
ID: 463818 • Letter: R
Question
Rocky Mountain Tire Center sells 14,000 go-cart tires per year. The ordering cost for each order is $35, and the holding cost is 40% of the purchase price of the tires per year. The purchase price is $23 per tire if fewer than 200 tires are ordered, $19 per tire if 200 or more, but fewer than 8,000, tires are ordered, and $14 per tire if 8,000 or more tires are ordered. How many tires should Rocky Mountain order each time it places an order? Rocky Mountain's optimal order quantity is units (enter your response as a whole number).Explanation / Answer
The optimal quantity in this case is based on the total cost (holding and ordering) plus the total cost of material.
First of we calculate the EOQ to find the optimal order quantity . EOQ will be determined using iteratvie process, starting with the first slab price.
EOQ = (2*annual demand*ordering cost/holding cost)^0.5 = (2*14000*35/(40%*23))^0.5 = 326
EOQ is more than 200, which means next slab of price is applicable, i.e. 19 .
So, EOQ = (2*14000*35/(40%*19))^0.5 = 359 .
Now we calculate the annual material cost, annual inventory holding and ordering cost and compare that with the cost associated with the lowest price slab, i.e. $ 14 price and 8000 order quantity.
Costs associated with EOQ model
Ordering cost = 14000/359*35 = 1365
Holding cost = 19*40%*359/2 = 1365
Material cost = 19*14000 = 266,000
Total cost = 268,729
Next we calculate the cost associated with the lowest price slab, i.e. $ 14 price and 8000 order quantity.
Ordering cost = 14000/8000*35 = 61.25
Holding cost = 14*40%*8000/2 = 22400
Material cost = 14*14000 = 196,000
Total cost = 218,461
The total cost is lowest in case of the price $ 14 and order quantity 8000 . Therefore optimal order quantity = 8000 units
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