Question

Rocky Mountain Tire Center sells 13 comma 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 $22 per tire if fewer than 200 tires are ordered, $18 per tire if 200 or more, but fewer than 5 comma 000 , tires are ordered, and $16 per tire if 5 comma 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). b) What is the total cost of this policy? Total annual cost of ordering optimal order sizeequals $ _____(round your response to the nearest whole number).

Answer 1

Optimal order quantity Q

Given Demand D = 13000

Ordering cost S = $35

Holding cost = 40% of the purchase price

Range	Price P	Holding cost H
< 200	$22	=0.4*22 = 8.8
>=200 <5000	$18	=0.4*18=7.2
>5000	$16	=0.4*16=6.4

EOQ at P =22

  

Q = 321.57 or 322 tires (NOT FEASIBLE)

EOQ at P =18

  

Q = 355.52 or 356 tires (FEASIBLE)

EOQ at P =16

  

Q = 377 (NOT FEASIBLE)

It is feasible at Q = 356 at p = 18

But we caculate total cost P= 18,Q= 356 and P= 16 and Q=5000

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

Total cost (P= 18,Q= 356) = (18*13000) +( 13000/356)35 + (356/2) *7.2= $ 236560

Total cost ( P= 16 and Q=5000) = (16*13000 + (13000/5000)35 + (5000/2)*6.4 = $224091

The cost is low at Q =5000

a) Rocky Mountains Optimal order quantity is 5000 units

b) Total cost = $224091