In general I would suggest to separate them especially if their melting temperature are so different.
But if you really want to mix them, first when you design the primers you shouldn't make their temperature too different (5oC different is the common guideline) otherwise it would be a bad idea to mix them because either you lost one of the product or getting some unspecific bindings. Then I would suggest the gradient to find the best temperature for them, but you could start with 5 degree below the lowest Tm primer.
In general I would suggest to separate them especially if their melting temperature are so different.
But if you really want to mix them, first when you design the primers you shouldn't make their temperature too different (5oC different is the common guideline) otherwise it would be a bad idea to mix them because either you lost one of the product or getting some unspecific bindings. Then I would suggest the gradient to find the best temperature for them, but you could start with 5 degree below the lowest Tm primer.
usully when you design your primers you select those who run with similar temperature to be running in one PCR. But try to do graduation first and then I advice you to run primers that works with same condition in PCR otherwise there is no way but to do your PCR in separate reactions for each sample.
I agree with Russel and suggest play with temp gradient and try to find the best annealing temperture to all your primers. Of course, you should start with temperature 5 °C below the lowest Tm, but I would not be afraid to raise the temp gradually up to 5 °C above the highest Tm. This worked well for my big and complicated (filaggrin) gene.
I agree with Russell, Irene and Elena. But do not be afraid of choosing a higher annealing temperature for the gradient PCR. Ta should be at least 5°C higher as the lowest primer Tm. Nevertheless it stays a little bit tricky with ARMS. Good luck ;)
I should add something on top of what you guys all said. there are some PCR master mixes which you dont need to run with different annealing temps. all primers could be run with the same temp even if you have designed them all with different annealing temps. here is what we use in our lab.
but please just be mindful to first run with some non-precious samples then use it on the precious ones. as far as I have tested it works well on primers with 5 c temp difference. hope it helps.