Rocky Mountain Tire Center sells 15,000 ?go-cart tires per year. The ordering co

Question

Rocky Mountain Tire Center sells 15,000 ?go-cart tires per year. The ordering cost for each order is ?$40?, and the holding cost is 30?% of the purchase price of the tires per year. The purchase price is ?$25 per tire if fewer than 200 tires are? ordered, ?$19 per tire if 200 or? more, but fewer than 5, 000? tires are? ordered, and ?$13 per tire if 5, 000 or more tires are ordered. What is the total cost of this? policy? Total annual cost of ordering optimal order size = ____ ?(round your response to the nearest whole? number).

Explanation / Answer

Ans:- Total cost = Annual ordering cost + Annual holding cost

= (D/Q)*S + (Q/2)*H

Where,

D: Annual Quantity Demanded

Q: Volume per Order

S: Ordering Cost (Fixed Cost)

H: Holding Cost (Variable Cost)

If 200 tires are ordered:-

Holding cost = 30% of purchase price = 0.3*19 = 5.7

So, Total cost = (15000/200)*40 + (200/2)*5.7 = $3570

Economic order quantity = Square root of (2*S*D/H) = Square root of (2*40*15000/5.7) = 458.8 = 459

Similarly, if 5000 tires are ordered,

Holding cost = 30% of purchase price = 0.3*13 = 3.9

So, Total cost = (15000/5000)*40 + (5000/2)*3.9 = $9870

Economic order quantity = Square root of (2*S*D/H) = Square root of (2*40*15000/3.9) = 554.7 = 555

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