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Working with loud speaker systems

The theatre is putting on a new musical and they are changing from traditional rifle microphones to radio microphone system. The theatre has some concerns over doing this, they are: transmitter operation with regard to power supplies, inter-modulation problems and choice of transmitter frequency band and output power.

Please can you help me with this problem. I have a list of equipment below if it helps you.

15 SK 50 VHF pocket transmitters (5 additional SK for instruments)
5 MKE 2 clip-on mics
3 EM 1046 systems
Mikroport system
1 Cadac J-type mixing console (72-inputs, 12 matrix and 24 matrix outputs)
41 loudspeaker system

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Solution with all explanations and mathematical steps.