pleas do come up with a suggestions. It would be nice if I could give the Board a kind of answer to how this can be done. Then they can decide how much money they whant to spend on it. Maybe it can be put into the next year's budget
Ok first and foremost, let me repeat, do not depend on this, get yourself a skilled operator or if you are teaching this, teach them how to do this manually and not to depend on this. I say this as someone that does teach this topic at the moment.
If you however absolutely want to do this route, the first thing you will need is a console that is capable of being remote controlled. On the analog side of things, this tends to happen on the mid to upper end of the range, starting at a few thousand USD and going up from there, so you are probably looking at an analog console that will cost a few thousand Euro if not more is my guess, but I am not to familiar with the going prices on that side of the pond.
If you go digital, most, if not all, digital consoles that are sold today have this functionality, even the cheap ones. However I would caution you strongly against going to cheap on this, specifically stay away from the Presonus StudioLive or cheaper consoles. I know some people that do mix on an O1V, personally I detest doing live mixes on that console. It can work in a pinch though.
The cheapest digital console I would recommend for live theater is the LS9. The LS9-16 has 16 mic preamps built in, so you would at the very least need some additional preamps(The LS9-16 can handle up to 32 channels). Alternatively, and typically a better bet for live mix, is the LS9-32 which has 32 mic preamps on it.
All this being said, personally I am not a huge fan of the LS9 either, and typically will recommend going larger. The M7CL for instance is a staple digital console in many theaters around the world, personally I feel it is getting a bit long in the tooth, but should still be considered for this reason. The PM5D is typical for larger shows. You can also look at offerings from Digico etc. but typically for theater uses you would want to make sure the scene recall and storage is robust enough, not all are.
At any rate given the above information, you can do what you want in one of two ways, or a combination of both. You can either use whatever built in scene storage and recall exists on the board to mute and unmute channels, or you can use a computer to control the console via MIDI. A good program to look at for this is Palladium on Windows, which is written by a theatrical sound designer specifically to control consoles in this fashion, and for digital consoles is often much more robust as well.
Alternatively I have done similar things with much more work in a variety of programs, most that can generate MIDI will work, so QLab and Live both I have done similar with, and there are many other options out there as well.
But just in case I wasn't clear enough yet, you should always depend on your board op to ride fader levels, and fade channels in and out rather than depending on mute scenes, and if mute scenes are used, they are only ever used as a backup AFTER the fader is brought down, or before it is brought up. Can you tell I am very adamant about this yet? ;)