Sarah and her fiancé are planning for their wedding. Distribution of the number of guests coming to the party is normal with the mean 100 and the standard deviation 10. They need to determine how many guests to book for food from a caterer. The caterer makes the following charges: $50 for each guest that is booked in advance; $90 for each guest who is not booked in advance but shows up on the wedding day. The caterer does not offer any refund even if some booked guests may not show up.                                                         Questions: What is the optimal number of guests to book in advance? How much Sarah can save by booking the optimal quantity from a) in advance? What is the expected number of guests that will come to their wedding? If Sarah and her fiancé book 90 guests in advance with the caterer, what is the probability of stock out? If Sarah and her fiancé book 100 guests in advance with the caterer, what is the expected number of meals to be wasted?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Sarah and her fiancé are planning for their wedding. Distribution of the number of guests coming to the party is normal with the mean 100 and the standard deviation 10. They need to determine how many guests to book for food from a caterer.

The caterer makes the following charges: $50 for each guest that is booked in advance; $90 for each guest who is not booked in advance but shows up on the wedding day. The caterer does not offer any refund even if some booked guests may not show up.                                                        

Questions:

  1. What is the optimal number of guests to book in advance?
  2. How much Sarah can save by booking the optimal quantity from a) in advance?
  3. What is the expected number of guests that will come to their wedding?
  4. If Sarah and her fiancé book 90 guests in advance with the caterer, what is the probability of stock out?
  5. If Sarah and her fiancé book 100 guests in advance with the caterer, what is the expected number of meals to be wasted?
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