INEN 455 Fall 2017 Homework 7 Released on 11/08/2017 Due by 11/15/2017 10am (in
ID: 366524 • Letter: I
Question
INEN 455 Fall 2017 Homework 7 Released on 11/08/2017 Due by 11/15/2017 10am (in hard copy 8. Billy's Bakery bakes fresh bagels each morning. The daily demand for bagels is a random variable with a distribution estimated from prior experience given by Number of Bagels Sold in One Day 10 15 20 25 30 35 Probability .05 10 10 20 .25 15 10 .05 The bagels cost Billy's 8 cents to make, and they are sold for 35 cents each. Bagels unsold at the end of the day are purchased by a nearby charity soup kitchen for 3 cents each. a. Based on the given discrete distribution, how many bagels should Billy's bake at the start of each day? (Your answer should be a multiple of 5.) 9. The Crestview Printing Company prints a particularly popular Christmas card once a year and distributes the cards to stationery and gift shops throughout the United States. It costs Crestview 50 cents to print each card, and the company receives 65 cents for each card sold. Because the cards have the current year printed on them, those cards that are not sold are generally discarded. Based on past experience and forecasts of current buying patterns, the probability distribution of the number of cards to be sold nationwide for the next Christmas season is estimated to be Quantity Sold 100,000-150,000 150,001-200,000 200,001-250,000 250,001-300,000 300,001-350,000 350,001-400,000 400,001-450,000 Probability 10 .15 .25 .20 15 10 .05 Determine the number of cards that Crestview should print this year Note: Question 8. (10 points) Question 9 (10 points). This is a group assignment with group discussion. Each group should have no more than 4 group members. Hint: Read through Chapter 5.1-5.3Explanation / Answer
Cost of shortage (Cs) = Sell price - Cost price = 35 - 8 = 27
Cost of excess (Ce) = Cost price - Salvage cost = 8-3 = 5
Service level = Cs/(Cs+Ce) = 27/(27+5) = 0.84
Hence, desired Service level is 0.84
Number of Bagels Sold and the cumulative probability:
Thus, 25 Bagels will give atleast 85% service level. So, it is the desired level
Bagels Probability Cumulative probability 0 0.05 0.05 5 0.1 0.15 10 0.1 0.25 15 0.2 0.45 20 0.25 0.7 25 0.15 0.85 30 0.1 0.95 35 0.05 1