Rocky Mountain Tire Center sells 7,000 go-cart tires per year. The ordering cost
ID: 368132 • Letter: R
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 30% of the purchase price of the tires per year. The purchase price is $23 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 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 this policy ?
Explanation / Answer
Total cost = Order cost + Holding cost + Purchase cost
Purchase cost
<200 =$23
200-5000 = $19
>5000=$16
Ordering cost =$40
Annual Demand = 7000 tires
Holding cost = .30*purchase cost
Q1*
=square root[ (2*7000*40)/(.30*23)]
=284.885
2.At $19
Q2*=square root[ (2*7000*40)/(.30*19)]
=313.441
3.At $16
Q3*=square root[ (2*7000*40)/(.30*16)]
=341.56
Of this only Q2* falls in the ordering qty limits(here 342 falls between 200and 5000) for the given price point.
A) So ordering quantity = 314( rounded) at $19 per unit
b)Total cost
Annual ordering cost = no. of orders placed in a year x cost per order
= annual demand/order quantity x cost per order
Annual ordering cost = 7000/314*$40 = 23 order* $40 per order = $920
Annual holding cost = average inventory level x holding cost per unit per year
= order quantity/2 x holding cost per unit per year
Annual holding cost =(314/2)*.3*19=$894.9
Purchase cost = 7000*$19 = $133000
Total cost = Order cost + Holding cost + Purchase cost
=$920 + $894.9 + $133000
=$134814.9 for the whole year
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.