Exhibit 12.5 The Following Questions Use the Information Below

question 7

Essay

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
-Jim Johnson operates a bus service to take college students to "The Big City" on Friday night and bring them back to school on Sunday night. The bus has 45 seats but sometimes there are empty seats. His records show that about 5% of ticket holders do not show up for their ride. Tickets cost $20 and are non-refundable. If Jim overbooks the bus and more than 45 passengers show up, some of them will be bumped and have to miss the trip. This bumping costs the company $40 because Jim has a double-your-money back policy for bumped passengers. Jim plans to accept 48 reservations (overbook 3 seats). What is Jim Johnson's expected marginal profit?

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Definitions:

Cosine

A mathematical function used in trigonometry to define the ratio of the adjacent side to the hypotenuse of a right-angled triangle.

Sine

A trigonometric function denoting the ratio of the length of the side opposite to a given angle to the length of the hypotenuse in a right-angled triangle.

Pulsating

A periodic variation in magnitude or intensity, often used to describe waveforms or signals.

Peak-to-peak

A measure of the amplitude of a waveform, indicated by the difference between its maximum and minimum values.