Large settlements require large threshold to support all the functions, but since the pizza business involves retailing low order goods, I would suggest a low threshold due to the regularity and frequency. After obtaining the population sizes for the different cities and towns in the state of Arizona, it seems the thresholds vary due to the difference in population size and the current number of restaurants in those cities and towns.
Given the level of competition in each city and town for the selected locations, the average threshold should be 3324, taken for the entire data provided in table 1.2 below. Therefore, this means the thresholds for Phoenix, Surprise, Yuma, Douglas, and Dewey can decrease, meaning market potential. Decreasing the threshold translates to adding more restaurants since the restaurant tries to fetch a lower threshold.
The Number of persons per restaurant = Total population of the location (city, town) Number of restaurant in that location
The average (recommended threshold) for the entire Arizona state = 2739361 . 824
This is the total population in the entire locations chosen divided by the total number of restaurants.
Kuby, M., Harner, J., & Gober, P. (1998). Human geography in action. New York: Wiley.