Question

Rocky Mountain Tire Center sells 5,000 ​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 25 per tire if fewer than 200 tires are​ ordered, 18 per tire if 200 or​ more, but fewer than 5,000​, tires are​ ordered, and 17 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

b) What is the total cost of ordering optimal order size with this order quantity, annually?

Answer 1

Since the holding cost varies with Price of the tire, we will have to find Economic order quantity for each price as shown below:

Annual Demand = D = 5000 tires

Ordering cost = S = 35

Holding cost = 30%

For Price P = 25,

Holding cost = 30% * 25 =H1 = 7.5

Economic order quantity EOQ = = = 216.02 = 216 tires

This quantity > 200 tires which is the maximum limit for P = 25. Hence, this EOQ is not feasible for < 200 tires, P = 25. Hence, the maximum quantity that can be ordered for P = 25 is 200 tires

For Price P = 18,

Holding cost = 30% * 18 =H2 = 5.4

Economic order quantity EOQ = = = 254.59 = 255 tires

This quantity > 200 tires and < 5000 which is within limit for P = 18. Hence, this EOQ is feasible for P = 18

For Price P = 17,

Holding cost = 30% * 17 =H3 = 5.1

Economic order quantity EOQ = = = 261.97 = 262 tires

This quantity < 5000 which is outside limit for P = 17 where Q required > 5000. Hence, this EOQ is not feasible for P = 17. Minimum quantity to be ordered = 5000 units

Hence,

Option 1: For P = 25, Q = 200

Option 2: P = 18, Q = 255

Option 3: P = 17, Q = 5000

We find total cost each option:

Option 1:

Total cost = Ordering cost + Holding cost + Purchase cost = = = 875 + 750 + 125,000 = $1,26,625

Option 2:

Total cost = Ordering cost + Holding cost + Purchase cost = = = 686.27 + 688.5‬ + 90,000 = $91,374.77‬

Option 3:

Total cost = Ordering cost + Holding cost + Purchase cost = = = 35 + 12,750‬‬ + 85,000 = $97,785‬

As seen from above, tghe lowest cost is for Q = 255 units

Hence,

a) Rocky Mountain's optimal order quantity is 255 units

b) The total cost of ordering optimal order size with this order quantity, annually = $91,374.77‬

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