Rocky Mountain Tire Center sells 8,000 go-cart tires per year. The ordering cost
ID: 343764 • Letter: R
Question
Rocky Mountain Tire Center sells 8,000 go-cart tires per year. The ordering cost for each order is $35, and the holding cost is 30% of the purchase price of the tires per year. The purchase price is $21 per tire if fewer than 200 tires are ordered, $17 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. a) How many tires should Rocky Mountain order each time it places an order? Rocky Mountain's optimal order quantity is 8000 units (enter your response as a whole number) Total annual cost of ordering optimal order size round your response to the nearest whole number)Explanation / Answer
Annual demand (D) = 8000 tires
Ordering cost (S) = $35
Order quantity price Holding cost (30% of price)
Fewer than 200 $21 $6.3
200-8000 $17 $5.1
More than 8000 $14 $4.2
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 $14 = sqrt of (2DS /H) = sqrt of [(2 x 8000 x 35)/4.2] = 365 tires. As an order quantity of 365 tires will cost $17 instead of $14, it is not a feasible point.
Minimum point for price of $17 = sqrt of (2DS /H) = sqrt of [(2 x 8000 x 35)/5.1] = 331 tires. Since an order quantity of 331 tires will cost $17,it is a feasible point
With order quantity (Q) = 331 units,
Total cost = Ordering cost + Holding cost + purchase cost
= [(D/Q) S] + [(Q/2)H] + (price x D)
= [(8000/331)35] + [(331/2)5.1] + (17 x 8000)
= $845.92 + $844.05 + $136000
= $137689.97
Minimum order quantity needed to obtain a price of $14 is 8000 units. So with order quantity(Q) = 8000 units,
Total cost = Ordering cost + Holding cost + purchase cost
= [(D/Q) S] + [(Q /2)H + (price x D)
= [(8000/8000)35] + [(8000/2)4.2] + (14 x 8000)
= $35 + $16800 + $112000
= $128835
a) Since the total cost when ordering 8000 per order is less than the total cost of ordering 331 per order, Rocky Mountain tire center's optimal order size is 8000 units.
b) Total annual cost of ordering Optimal order size is $128835
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