Question

Rocky Mountain Tire Center sells 7,000

?go-cart tires per year. The ordering cost for each order is

?$40?,and the holding cost is

40?%

of the purchase price of the tires per year. The purchase price is

?$20

per tire if fewer than

200

tires are? ordered,

?$19

per tire if

200

or? more, but fewer than

5,000 tires are? ordered, and ?$16 per tire if

5,000 or more 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?

Answer 1

We calculate the EOQ , it comes to be 272 (but that is in 2nd range)

So we calclulate for each margin of the change of price, ie border conditions and so we get the below table.

D	Demand	7000	7000	7000	7000	7000	7000	7000	7000
K	Ordering cost	40	40	40	40	40	40	40	40
h = .4*P	holding cost	8	8	7.6	7.6	7.6	6.4	6.4	6.4
P	Price	20	20	19	19	19	16	16	16
Q=Sqrt(2KD/h)	Order Qty	100	199	271.4484	4999	200	5000	5001	6000
Q*h/2	Holding cost	400	796	1031.504	18996.2	760	16000	16003.2	19200
D*k/Q	Ordering cost	2800	1407.035	1031.504	56.0112	1400	56	55.9888	46.66667
D*P	Product cost	140000	140000	133000	133000	133000	112000	112000	112000
Sum	Total cost	143200	142203	135063	152052.2	135160	128056	128059.2	131246.7
							Lowest

So we see the lowest total cost comes at Q= 5000

And the cost for it is 128056