Rocky Mountain Tire Center sells 20,000 go-cart tires per year. The ordering cost for each order is $40, and the holding cost is 20% of the purchase price of the tires per year. The purchase price is $20 per tire if fewer than 500 tires are ordered, $18 per tire if 500 or more—but fewer than 1,000—tires are ordered, and $17 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?

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

b) What is the total cost of this policy?

Explanation:

we must find the EOQ for the three possible prices:

when price per tire is $17:

EOQ = √(2SD) / H

S = cost per order = $40

D = annual demand = 20,000

H = 20% x $17 = $3.40

EOQ = √[(2 x $40 x 20,000) / $3.40] = 685.99 = 686 tires

when price per tire is $18:

EOQ = √(2SD) / H

S = cost per order = $40

D = annual demand = 20,000

H = 20% x $18 = $3.60

EOQ = √[(2 x $40 x 20,000) / $3.60] = 666.67 = 667 tires

when price per tire is $20:

EOQ = √(2SD) / H

S = cost per order = $40

D = annual demand = 20,000

H = 20% x $20 = $4

EOQ = √[(2 x $40 x 20,000) / $4] = 632.46 = 632 tires

since all options are over 500 units but lower than 1,000, we must take the option where each tire costs $18

total cost:

20,000 x $18 = $360,000

(20,000 / 667) x $40 = $1,199.40

holding costs = average inventory = 667 / 2 = 333.5 x $3.60 = $1,200.60

total costs (including merchandise purchased) = $362,400

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%