# Ticketing Options

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Where there exists a fixed number of seats, as in a theater, concert hall, or stadium, the seats are usually assigned to categories having different ticket prices. A difficulty in optimizing the seats' breakdown may arise if the occupancy at each price category can only be guessed or estimated. This Demonstration shows how the expanded Fermi solution can be used to examine different ticketing options and assess their impact on the total sales.

Contributed by: Mark D. Normand and Micha Peleg (October 2014)
Open content licensed under CC BY-NC-SA

## Details

Snapshot 1: ticket sales to an event with equal allocation of seats to each price category

Snapshot 2: ticket sales to an event with fewer seats allocated to the highest and lowest price categories

Snapshot 3: ticket sales to an event with smaller price differences between categories

Consider a venue with a given number of seats divided into four ticket price categories, 1, 2, 3, and 4. The total sales of tickets to this event or show is the sum of the number of seats sold in each category multiplied by the seats' corresponding ticket price. Unless the event or show is always fully sold out, the occupancy in each category is unknown a priori and hence needs to be guessed or estimated. In this Demonstration, the fraction of a category's seats that are occupied is chosen at random from the interval , ]. Once this choice is made, the revenue from ticket sales can be computed. The distribution of this revenue is nearly normal as can be seen from the histogram made from many observations of this revenue superimposed on a normal distribution.

Since some seat allocations do not add up to the total number of seats, a setter to assign the remaining seats to the fourth category has been added.

To eliminate a price category, assign zero to its number of seats.

To avoid exceeding the assigned ranges on the number of seats when increasing or decreasing the total number of seats, it is easier to set all four seat-count sliders to zero before entering the new values and leaving category 4 to be the last entered.

The purpose of the Demonstration is only to present the principle. Thus, it cannot be applied in its present form where more than four price categories, larger price ranges, or larger venues are considered. However, these can be accommodated with minor changes in the code.

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