The Game Studio, which is available only when you get to Level 30, is a chain quest which enables you to increase your maximum tourist  count AND to get potions! Once Level 30 is reached, a building under construction will appear next to your Tour Center.

Game Studio 1

Once built, the chain quest begins with tasks for you to complete. Upon completion of a task, another one will appear until you the quest is completed. It takes a little while for a new task to appear at each step so do be patient. When a new task appears, an alert icon will appear over the studio.
Game Studio 8
The following lists the tasks needed to complete this quest.
Game Studio
Game Studio 2
Game Studio 3
Game Studio 4
Game Studio 5
Game Studio 6
Game Studio 7
A total of 56 new tourists will be visit your property upon completion of these tasks!