Final answer:
Geographers determine the profitability and optimal location for a service through site location analysis, economic base analysis, and considering factors of production.
Step-by-step explanation:
Geographers use various methods to determine the profitability and optimal location for a service. One approach is site location analysis, where factors such as traffic patterns, real estate costs, zoning laws, economic competition, and demographics are analyzed using tools like Geographic Information Systems (GIS).
Another method is economic base analysis, which uses the location quotient formula to identify industries that bring in money from outside the local economy. Lastly, business geographers consider factors of production like land, labor, and capital to assess the costs and profitability of locating a business or factory.