Break-Even Calculations and Probabilities

The assignment content includes two chapters with problems on break-even analysis and probability theory. In Chapter 1, Problem 22 calculates the number of people needed by Golden Age to break even, concluding that at least 45 people must attend each seminar. Problem 23 calculates the number of students needed to break even in a smaller room possibility, finding that 14 students are required. In Chapter 2, Problem 43 calculates the probability of exactly 0 to 5 arrivals per day and finds that the sum is less than 1 due to probabilities for more than 5 arrivals. Problem 45 calculates the expected time between arrivals (0.33 hours) and variance of the time between arrivals (0.11 hours).

Chapter 1 - Problem 22
The calculation of number of people needed by Golden Age to break even is as shown below:
Since, people cannot be 44.24 hence, at least 45 people must attend each seminar so that the
break even condition met.
Chapter 1 - Problem 23
(a) The calculation of number of students needed to break even is as shown below:
Therefore, 19 students must enrol so that the break even condition met.

(b) The calculation of number of students needed to break even when smaller room
possibility is considered is as shown below:
Therefore, 14 students must enrol so that the break even condition met.
Chapter 2- Problem 43
(a) The calculation of probability of exactly 0, 1, 2, 3, 4, and 5 arrivals per day in Excel is as
shown below:

(b)
The sum of these probabilities in Excel is calculated as follows:
This sum is less than 1 because arrivals more than 5 also have some probabilities associated
with them. The sum of all the probabilities from zero to infinity arrivals will be equal to 1.
Chapter 2 - Problem 45
(a) The formula to calculate the expected time between arrivals is as written below:
The calculation in Excel is as shown below:

Therefore, the expected time between arrivals is 0.33 hours or it can be also written as:
(b) The formula to calculate the variance of the time between arrivals is as written below:
The calculation of variance in Excel is as shown below:
Therefore, the variance of the time between arrivals is 0.11 hours or it can be also written as: