Question

Rocky Mountain Tire Center sells 13,000 ?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, ?$16 per tire if 200 or? more, but fewer than 5 comma 000?, tires are? ordered, and ?$14 per tire if 5,000 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 ______ units ?(enter your response as a whole? number).

Answer 1

Optimal order quantity Q

Given Demand D = 13000

Ordering cost S = $35

Holding cost = 30% of the purchase price

Range	Price P	Holding cost H
< 200	$21	=0.3*21 = 6.3
>=200 <5000	$16	=0.3*16=4.8
>5000	$14	=0.3*14=4.2

EOQ at P =21

  

Q = 380 tires (NOT FEASIBLE)

EOQ at P =16

  

Q = 435.41 or 435 tires (FEASIBLE)

EOQ at P =14

  

Q = 465 (NOT FEASIBLE)

It is feasible at Q = 436 at p = 16

But we caculate total cost P= 16,Q= 436 and P= 14 and Q=5000

Total cost = PD + (D/Q)S + (Q/2)H

Total cost (P= 16,Q= 436) = (16*13000) +( 13000/436)35 + (436/2) *4.8= $ 210090

Total cost ( P= 16 and Q=5000) = (16*13000 + (13000/5000)35 + (5000/2)*6.4 = $183006.6

The cost is low at Q =5000

a) Rocky Mountains Optimal order quantity is 5000 units