Question

Foxie Owl’s Besty Bagel shop makes fresh bagels. She has to buy raw materials fresh every day for selling on that day, and she wants to know exactly how much should she spend on raw materials. She did some analysis over the past month and came back with the following figures:

• daily demand was equally likely to be 100, 125, 150, 175, or 200 bagels
• fresh bagels could be sold at $4 each
• day-old bagels are sold at $1.50 each at the end of the day
• raw materials for each bagel is estimated at $2.50
• to make all customers happy, Foxie Owl gives a 25 cent discount coupon to each lost customer when she’s out of bagels, for use next time

Use this information to answer the following 9 questions.

1. What is the probability that Foxie has orders for exactly 150 bagels on a given day?

2. What is the probability that Foxie has orders for 175 bagels or less, on a given day? (Provide your answer up to two decimal points, not as a percentage.)

3. What is the probability that Foxie has orders for exactly 145 bagels on a given day?

4.What is the mean demand for Foxie's bagels on a given day?

5.If Foxie wants to maintain a 90% service level, how many bagels should Foxie keep in opening inventory every day?

6.If Foxie wants to maintain a 90% fill rate, how many bagels should Foxie keep in opening inventory every day?

7.If Foxie keeps a starting inventory of 125, how many expected units of demand will get unmet?

8.If Foxie keeps a starting inventory of 125, how many expected units will remain in inventory as leftover?

9. If Foxie keeps a starting inventory of 125, how many expected units will be sold?

Answer 1

(since there are more than 4 parts i will answer first 4)

demand was equally likely to be 100, 125, 150, 175, or 200 bagels

therefore probability for each demand is p = 1/5

1. Probability that Foxie has orders for exactly 150 bagels on a given day

p(150 bagels demand) = p = 1/5 = 0.2

2. Probability that Foxie has orders for 175 bagels or less

P(demand 175 or less) = p(100) + p(125) + p(150) + p(175)

= 1/5 + 1/5 + 1/5 + 1/5

P(demand 175 or less) =  0.8

3. Probability that Foxie has orders for exactly 145 bagels

P(demand = 145) = 0

{beacuse it is not in 100, 125, 150, 175, or 200 }

4. Mean demand for Foxie's bagels on a given day

mean = sum of (x*P(x)) {x = demand}

mean = 0.2*100 + 0.2*125 + 0.2*150 + 0.2*175 + 0.2*200

= 20 + 25 + 30 + 35 + 40

mean = 150

P.S. (please upvote if you find the answer satisfactory)