Rocky Mountain Tire Center sells 5,000 go-cart tires per year. The ordering cost
ID: 465333 • Letter: R
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 $24 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 $13 per tire if 5,000 or more tires are ordered. 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). 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
We have following information
Annual demand D= 5000 go-cart tires per year
Ordering cost S = $ 35 per order
Holding or carrying cost H = 30% of purchase price
Case 1: The purchase price = $24 if tire ordered less than 200
Case 2: The purchase price = $16 if tire ordered between 200 to 5000
Case 3: The purchase price = $13 if tire ordered more than 5000
Holding or carrying cost H in Case 1,
30% of $ 24 = $ 7.2
Holding or carrying cost H in Case 2,
30% of $ 16 = $ 4.8
Holding or carrying cost H in Case 3,
30% of $ 13 = $ 3.9
For minimum cost, first we have to calculate Optimum Order quantity per order which is EOQ
Case 1: EOQ = sqrt (2* D*S/H) = sqrt(2*5000*35/7.2) = 220.45 units
Case 2: EOQ = sqrt (2* D*S/H) = sqrt(2*5000*35/4.8) = 270.03 units
Case 3: EOQ = sqrt (2* D*S/H) = sqrt(2*5000*35/3.9) = 299.57 units
Total Annual Inventory cost = total ordering cost + total carrying cost
Case 1: Total Annual Inventory cost = (D/Q)* S + (H*Q)/2
= (5000/220.45)*35 + (7.2*220.45)/2 = $ 1,587.45
Case 2: Total Annual Inventory cost = (D/Q)* S + (H*Q)/2
= (5000/270.03)*35 + (4.8*270.03)/2 = $ 1,296.15
Case 3: Total Annual Inventory cost = (D/Q)* S + (H*Q)/2
= (5000/299.57)*35 + (3.9*299.57)/2 = $ 1,168.33
As the total cost is lowest in case three therefore for Rocky Mountain the optimal order quantity is 299.57 or 300 units
And total cost of this optimal order is $ 1,168
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