License models

Well, Concurrent may be academic unless you are upgrading from V9, but in the Concurrent model a "user" is:

A. A Client Device – Client Devices include, but are not limited to, workstations, personal computers, PDA devices,
cellular phones and laptops that are operated by a human.
B. A Non-Human Operated Device – Non-Human Operated Devices include, but are not limited to, temperature
devices, production line bar code scanners and tracking devices.
C. A Server Process – A Server Process is any process that is not initiated by a Client Device or Non-Human
Operated Device. Server Processes include, but are not limited to, automated controls, background jobs or
automated processes.

So you have 10 of the first, assuming each human is at a different device, 5 or the second, and 4 of the third.  But:

The Concurrent User license count must be the greater of:
i. The peak number of Client Devices and Non-Human Operated Devices that simultaneously use an
OpenEdge client product or simultaneously use an application that can access an OpenEdge server product;
OR
ii. The peak number of Server Processes that can simultaneously use an OpenEdge server product.

So, the 4 server processes are not counted since there are fewer of them than the total of the other two, so you need 15 users, assuming that all of the users will be on at the same time.

Registered client uses the same definitions, but counts differently:

The Registered Client license count must be equal to the total number of Client Devices,
Non-Human Operated Devices and Server Processes that can use an OpenEdge client product or use an application
that can access an OpenEdge server product.

So in Registered Client, all of the users count so you have 19.

Named User alters the definitions slightly:

With the Named User model, a User can be:
A. A human.
B. A Non-Human Operated Device – Non-Human Operated Devices include, but are not limited to, temperature
devices, production line bar code scanners and tracking devices.
C. A Server Process – A Server Process is any process that is not initiated by a Client Device or Non-Human
Operated Device. Server Processes include, but are not limited to, automated controls, background jobs or
automated processes.

But, in your case, the difference in definition is immaterial since you have one human working at one machine, so the counts are the same.  As for counting:

The Named User license count must be equal to the total number of humans, Non-Human
Operated Devices and Server Processes that can use an OpenEdge client product or use an application that can
access an OpenEdge server product.

So, once again you have 19.

My understanding (not confirmed) is that those allowed to buy concurrent user licenses under OE10 are paying V9 prices.  Obviously, if you buy V9 and upgrade to OE10 and keep your concurrent user licenses, that is what you would pay.  V9 prices as of my last list are $250 for Workgroup and $730 for Enterprise so that would be $3750 or $10950 for 15 users.

Both Registered Client and Named User are $200 for Workgroup and $585 for Enterprise, so that would be $3800 or $11115 for 19 users, i.e., close enough as to make hardly any difference although applying the same figures to future growth might give you rather different results.

And, of course, there is that AppServer bit you are neglecting for now ...

Just wanted to mention that it is always a good idea to consult with your Progress Account Manager with your questions on licensing and pricing. They will be happy to work through the details with you, and to help you come up with the most cost-effective solution for your situation.

It can also be useful to have a second source ...

Always have as much information as possible before talking to a sales person.  Any sales person.