Question

Rocky Mountain Tire Center sells 6,000 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, $16 per tire if 200 or​ more, but fewer than 5,000, tires are​ ordered, and $15 per tire if 5,000 or more tires are ordered

​a) How many tires should Rocky Mountain order each time it places an​ order? (optimal order quantity)

b) What is the total cost of this​ policy?

Answer 1

a)

Annual demand, D = 6000

Ordering cost, S = $ 35

Considering purchase price, C= $ 22

Holding cost, H = 22*40% = $ 8.8

EOQ = SQRT(2DS/H)

= SQRT(2*6000*35/8.8)

= 218

This is greater than 200, Therefore applicable purchase price, C = $ 16

Revised holding cost, H = 16*.4 = $ 6.4

Revised EOQ = SQRT(2*6000*35/6.4)

= 256

Total annual Ordering, holding and purchase cost of EOQ policy

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

= (6000/256)*35 + (256/2)*6.4 + 6000*16

= $ 97,640

Considering the next level purchase price, C = $ 15, Holding cost, H = 15*.4 = $ 6, order quantity, Q = 5000

Total annual cost = (6000/5000)*35 + (5000/2)*6 + 6000*15

= $ 105,042

Total cost of EOQ policy is the lowest.

Therefore, optimal order quantity = 256 tires

b)

Total annual cost of this policy = $ 97,640