Question

Rocky Mountain Tire Center sells 22,000 go-cart tires per year. The ordering cost for each order is $45, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $25 per tire if fewer than 500 tires are ordered, $20 per tire if 500 or more—but fewer than 1,000—tires are ordered, and $18 per tire if 1,000 or more tires are ordered.

a. How many tires should Rocky Mountain order each time it places an order?

b. What is the total cost of this policy?

Please show all work/steps

Answer 1

Annual demand(D) = 22000 tires

Ordering cost (S) =$45

Holding cost(H) = 20% of purchase price

Order size Price per unit Holding cost(20% of price per unit)

0-500 25 5

500-1000 20 4

1000 or more 18 3.6

First find the minimum point for each price starting with the lowest price until feasible minimum point is located.This means until a minimum point falls in the quantity range for its price

Minimum point for price = Sqrt of (2DS/H)=Sqrt of [(2X22000X45)/3.6] = sqrt of 550000 = 742 tyres.Because an order size of 742 tyres will cost $20 rather than $18, 742 is not a minimum feasible point for $18 per unit.

Minimum point for price of $20 = Sqrt of (2DS/H) =Sqrt of [(2X22000X45)/4]= sqrt of 495000 = 704 tyres.This is feasible as it falls in the $20 per tyre range of 500-1000

Now the total cost for 704 tyres is computed and compred to the total cost of the minimum quantity needed to obtain price of $18 per tyre

Total cost for Q=704 is (Q/2)H + (D/Q)S + (PriceXD)

= [(704/2)4] + [(22000/704)45] + (20X22000)

= 1408 + 1406. 25 + 440000

= $442814.25

The minimum quantity needed to obtain a price of $18 is 1000 units.So with order quantity(Q) = 1000 units,

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

= [(1000/2)3.6] + [(22000/1000)45] + (18 x 22000)

= 1800 + 990 + 396000

= $398790

a) So Rocky mountain's optimal order quantity is 1000 units as it has the lowest total cost.so they should order 1000 tires each time

b) The total cost of ordering optimal order is $398790