Billy\'s Bakery bakes fresh bagels each morning. The daily demand for bagels is
ID: 3220705 • Letter: B
Question
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 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.) b. If you were to approximate the discrete distribution with a normal distribution, would you expect the resulting solution to be close to the answer that you obtained in part (a)? Why or why not? c. Determine the optimal number of bagels to bake each day using a normal approximation.Explanation / Answer
Solution:
c0 = 0.08 - 0.03 = 0.05
cu = 0.35 - 0.08 = 0.27
Critical ratio = 0.27/0.05+0.27 = 0.84375
From the given distribution, we have:
Q f(Q) F(Q)
0 0.05 0.05
5 0.10 0.15
10 0.10 0.25
15 0.20 0.45
20 0.25 0.70
< - - - - .84375
25 0.15 0.85
30 0.10 0.95
35 0.05 1.00
Since the critical ratio falls between 20 and 25 the optimal is Q = 25 bagels.
b)
m = åxf(x) = (0)(.05) + (5)(.10) +...+(35)(.05) = 18
s2 = åx2f(x) - m2 = 402.5 - (18)2 = 78.5
s = sqrt(((2)(32)(1032))/0.36) = 8.86
The z value corresponding to a critical ratio of .84375 is 1.01. Hence,
Q* = sz + m = (8.86)(1.01) + 18 = 26.95 ~ 27.
c) Type 2 service level (fill rate) for the solution in part is 85%
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.