On (minuscule) dark matter production in supernovae
The most favoured WIMPS at the moment are probably neutralinos, see
http://en.wikipedia.org/wiki/Neutralino

These particles are purely hypothetical at the moment.
The mass estimates in the above Wikipedia article for the lightest neutralino range between 
10 and 10,000 GeV, meaning that the production rates in SNs will be much lower than with an assumed 1 GeV.
Higher production rates should have already been detected at LHC.

Hence from the non-detection (in the form of energy loss) of WIMPS at LHC an estimate of an upper bound of the production rates in SNs should be possible.