Should I allocate MORE memory to the app or LESS in order for it to use less CPU? It is currently at the default 32mb min / 768mb max.
This demonstrates you have a fundamental misunderstanding of how computers work:
(a) On modern operating systems, the decision of how much memory to use is generally best left to the operating system
(b) Manually tweaking memory is not going to have any effect on CPU
How about you look at the low hanging fruit first ? i.e.
The number one consumer of battery is staring you in the face.
Yes really.
Ok, I'll spell it out. It's the monitor. Set it to the minimum brightness you need. If you're stepping away from the screen, turn the brightness right down to zero (or however low your laptop will go).
The number two consumer of battery ?
Radios.
Got bluetooth ? Not using it ? Turn it off.
Got 3G/4G/mobile data ? Not using it ? Turn it off.
Got Wifi ? Can you use a nearby CAT5/CAT6 cable instead (e.g. in a hotel room) ? Great. Use that, turn WiFi off.
Number three ?
USB
Using your laptop to charge your phone/tablet ? Stop it !
Got anything bus-powered that's more than a keyboard/mouse plugged in ? Take it out.
Number four ?
Hard drive.
If you're on good old-fashioned spinning metal, swap it for an SSD. No need to power that motor to spin the platters !
Once you've dealt with the low hanging fruit, then and only then should you start looking at your software options ....
Explore your operating system's energy saving settings
If you're on a windows box, look at the BIOS level energy savings settings
Running bloatware and other rubbish in the background ? Kill it
Un-necessary CPU hungry software open ? Kill it.