How is the maximum number of virtual machines a computer can run determined?

Nope. You can run as many as you want. They each would require some CPU power and some memory. For example if you have a Quad Core 3GHz processor you can divide it as 4 processor (physical) x 1GHz x 3 = 12 Virtual Machines of 1GHz processors. If you halve this processing lower you have 24 virtual machines. Remember your slicing must be cognizant of the OS requirement to run successfully.