A) Cruiser vs Heavy Cruiser
As written above, the mathematically perfect fleet included both cruisers and heavy cruisers. HOWEVER, it is not always advantageous to attack with both of them in your fleet. In fact, you will usually want to attack while leaving your heavy cruisers OUT. Reason for this? It's simple cost effectiveness. The cost/armor ratio of a heavy cruiser is fairly high, whereas the cost/armor ratio of a fighter/bomber/corvette/destroyer/cruiser is fairly low. Adding a ship (like the HC) to a shot when you don't HAVE to will cause higher losses than if you were to leave them out....EVERY time. In fact, the majority of your attacks that you make should not involve a ship larger than a cruiser for greatest cost effectiveness to minimize your losses. So when do you use cruisers, when do you use HC, and when do you use them both? Here's some situations to come across and what is normally advised:
Cruiser Situations (leave HC out of your attack fleet)
1) When attacking a fleet without ships higher than a DN in them
2) When attacking a base without several layers of planetary shield (if you have thousands or 10's of thousands of cruisers it doesn't matter what the base has, you'll punch through)
3) When you're NOT going to be able to "one shot" a fleet anyway
Heavy Cruiser Situations (leave Cruisers out of your attack fleet)
1) When attacking a fleet that has a very small amount of cruisers & below left AND contains Titans or Leviathans
2) When you are attacking a base with several layers of planetary shields and you do not have enough firepower without using heavy cruisers to one shot the base. It is almost always better to one shot a base than to take it in 2 shots.
Cruiser and Heavy Cruiser situations, when you should use BOTH in the same shot
1) When you want to spread your losses across both classes. There is almost no situation where it is best to mix cr/hc together for simple cost effectiveness. But sometimes, resupplying your fleet is time consuming, so you want to keep it "even" as much as possible. In these cases, it is sometimes best to sacrifice cost effectiveness for spreading the damage across 2 kinds of classes of ship. So if that happens, and you would rather lose a few HC and a few CR instead of losing more of one or the other, use them both and ignore the suggestions above