Question

A gourmet coffee shop in downtown San Francisco is open 200 days a year and sells an average of 75 pounds of Kona coffee beans a day.​ (Demand can be assumed to be distributed normally with a standard deviation of 15 pounds per​ day). After ordering​ (fixed cost​ = ​$16.00 per​ order), beans are always delivered from Hawaii in exactly 4 days.​ Per-pound annual holding costs for the beans are ​$3.00. Refer to the standard normal tableLOADING... for​ z-values. ​a) What is the economic order quantity​ (EOQ) for Kona coffee​ beans? 400 pounds ​(round your response to the nearest whole​ number). ​b) What are the total annual holding costs of stock for Kona coffee​ beans? ​$ 600 ​(round your response to the nearest whole​ number). ​c) What are the total annual ordering costs for Kona coffee​ beans? ​$ 600 ​(round your response to the nearest whole​ number). ​d) Assume that management has specified that no more than a 1​% risk of stockout during lead time is acceptable. What should the reorder point​ (ROP) be? nothing pounds ​(round your response to two decimal​ places).

Answer 1

Answer:

EOQ 400 units

inventory cost $1,200

 holding $600

 ordering $600

reorder point 369.9 pounds

Explanation:

EOQ

$Q_{opt} = \sqrt{\frac{2DS}{H}}$

Where:

D = annual demand =  200 days x 75 pound per day =  15,000  

S= setup cost = ordering cost = $         16

H= Holding Cost =                       $          3

$Q_{opt} = \sqrt{\frac{2(15,000)(16)}{3}}$

EOQ 400

Inventory cost:

average inventory x holding cost

400/2 x $3 = $600 holding cost

order per year x order cost

15,000/400 x $16 = $600 order cost

reorder point: demand x lead time + safety stock

to get a confidence of 99% we need to look at the table for a Z value which is above 99% of the cases and then, move it to our ditribution.

In the talbe we got at a Z of 2.33 has a score of 0.99 which is the probability we want.

Now we calculate the safety stock

$2.33 \sqrt{4\times 15^{2} }$

safety stock: 69.9

This is the safety stock

Now the company will reorder at:

daily use x lead time + safety stock:

75 x 4 + 69.9 =

300 + 69.9 = 369.9