I’m looking for what the most cost efficient way to balance a window unit with the existing central AC would be. On mobile so sorry for the formatting. Details below.

I’m renting a duplex at the moment, and the central AC is absolutely awful. How awful you ask? In the summer here, the AC unit will struggle to maintain 78F when it’s just 85F outside. And when it’s in the 90’s with warm night temperatures, that AC unit will run 24 hours a day to maintain something around 80-82F inside during the heat of the day. I live on the second floor of this duplex, it’s 1350sqft, the windows are all old and awfully insulated, the central AC is old as the dinosaurs. When I complained to the landlord about running the AC nonstop in the summer just to keep the place slightly below sweltering, they sent out an HVAC guy to look at it. The unit is working as designed. It’s just old as balls, and I don’t think it’s sufficient for the space. The HVAC guy recommended a few things, (cleaning vents changing filters, installing blinds over a few windows without coverings, etc...). The last thing that was recommended was getting a window unit, which the landlord supplied and installed this afternoon.

Now I can keep the temperature on the thermostat around a much more comfortable 75F with the two AC units working together, and the central AC isn’t running nonstop. So here’s the question: how do I run the two units together in the most energy efficient way to keep the place comfortable? Should I run the window unit at full boar to take the most of the heat load off of the central unit that I can? Should I find the warmest settings on the window AC unit that allows the central AC to just barely maintain a comfortable temperature while running throughout most of the day? Something in between? Should I keep both units on at night? Turn off the window unit at night? Etc...

Feel free to ask me any questions about my setup. I’m not super knowledgeable about any of this stuff, so I’m sure I probably left out a ton of pertinent information.