Question

A large hotel chain buys its cleaning supplies in bulk from a national vendor.  The hotal purchasing manager currently orders a multi-purpose cleanser used to  clean the guest bathrooms in quantities of 6,000 gallons at a time.  She is considering changing the order quantity to the EOQ.  The manager has collected the data in the table below.  Use the data to answer questions a-d below.  The hotel is open 365 days out of the year.
Inventory Information for Shower Cleanser
The Cost of a Gallon of the Cleanser	$9.95
Annual Holding Cost (as a % of Cost)	18%
Cost to Place an Order	$15.00
Average Daily Demand (in gallons)	1000
Current Order Quantity	6000
a)  What is the EOQ for the cleanser?
b)  What would the annual ordering cost be under the EOQ?
c)  What would the annual holding cost be under the EOQ?
d)  How much money would the company save annually if it switched to the EOQ?

Answer 1

Question: A large hotel chain buys its cleaning supplies in bulk from a national vendor. The hotal purchasing manager currently orders a multi-purpose cleanser used to clean the guest bathrooms in quantities of 6,000 gallons at a time. She is considering changing the order quantity to the EOQ. The manager has collected the data in the table below. Use the data to answer questions a-d below. The hotel is open 365 days out of the year.

Answer:

Given that:

Dalily Demand (d) = 1000

Number of working days (N) = 365

Ordering Cost (S) = 15

Unit Cost (C) = 9.95

Carrying Cost (I) = 18%

Annual Demand (D) = 1000 x 365 = 365000

Holding Cost (H) = I x C = 18% x 9.95 = 1.79

a) What is the EOQ for the cleanser?  

Economic Order Quantity (EOQ) is given by:

EOQ = Sqrt(2 x D x S / H)

Therefore:

EOQ = Sqrt(2 x 365000 x 15 / 1.79)

EOQ = Sqrt(6113902.85)

EOQ = 2472.63

b) What would the annual ordering cost be under the EOQ?  

Annual Ordering Cost is given by:

Annual Ordering Cost = (D x S) / EOQ

Therefore:

Annual Ordering Cost = (365000 x 15) / 2472.63

Annual Ordering Cost = 2214.24151612

Annual Ordering Cost = 2214.24

c) What would the annual holding cost be under the EOQ?  

Annual Holding Cost is given by:

Annual Holding Cost = (EOQ x H) / 2

Therefore:

Annual Holding Cost = (2472.63 x 1.79) / 2

Annual Holding Cost = 2213.00385

d) How much money would the company save annually if it switched to the EOQ?  

Annual Cost is given by:

Annual Cost = (D x S) / EOQ + (EOQ x H) / 2

For Current Quantity = 6000

Annual Cost = ((365000 x 15) / 6000) + ((6000 x 1.79) / 2)

Annual Cost = 6282.5   

For EOQ = 2472.63

Annual Cost = ((365000 x 15) / 2472.63) + ((2472.63x 1.79) / 2)

Annual Cost = 4427.24536612 = 4427.25

Now:

Annually Saved = Total Cost of Current Quantity - Total Cost of EOQ

Therefore:

Annually Saved = 6282.5 - 4427.25

Annually Saved = 1855.25

Therefore, about $1855.25 is saved annually if it switched to the EOQ.

Please Note: Decimals are rounded to two. Refer accordingly.