yes - Amber is right - do 5-10 minute cardio warm up - then weights. One of hte reasons as someone else mentioned is you need all your power to do the weights - that way you will get a much more effective weight lifting work out, your body is not tired yet. You all should be able to do cardio anytime now! It's easier

(not only did the trainer tell me to do it this way, but so did my bro the doctor (orthopod))
so the second question I also ponder is how do we make time for all of this? well technically you should not be doing weights every day - usually 3-4 times a week. You could split things up - like upper body then lower body and do one big day of all big muscle groups. or back and chest and abs then arms and legs.
And if you can't think of hopping on a machine after your weights, maybe think of switching your cardio routine untill you can - maybe take a class - or do the eliptical - or go on a track - or go swimming (if you are a strong swimmer! becaue it is harder to go swimming when your arms are tired - I tried this once - what a workout!) or do something with a friend - racquetball, tennis etc. remember cardio does not just mean go on a treadmill
jeez I sound like some magazine article or something - sorry! I need to work on getting my weights in better - it's hard though!