Connecting three monitors to one computer

A question from a reader:

I hate to bother you but I have been reading on the internet about the multi-screen topics you write about. If you have time to answer my question – I would greatly appreciate it.
I have been assigned what seems to be an impossible project – and given almost nothing as a budget.
My company want me to create a 3 TV set visual in our business.
I see where you write about similar set-ups – I had hoped you can give me some direction.
This is ULTIMATELY what I would like to make happen.
We have a computer that sits there and has little other purpose.
I would like to use this computer to drive 3 modern TV sets (which have perhaps VGA inputs). I see some links you provide to companies that make video splitting devices – but we would need the model that costs almost 2 thousand – which is my entire budget – so this won’t work. Anyway – I am looking for a cheap way to connect 3 TV sets to a computer AND have the computer to run 3 separate programs which will feed these 3 separate TV sets. I may be able to get this down to 2 TV’s – but 3 is the ultimate goal.
What have you seen or read about that is cheap that may be able to do what I need? I really would appreciate any advice you have on the subject.

And my answer:

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