Thrust reduction with varying conditions

[LA931]

I have a question that may seem pretty basic to most of you, but I can't figure it out.
I understand that thrust decreases as density decreases. That means that in warmer days or higher altitudes, maximum available thrust would be less than at sea level on a cold day.
Well, I have a Takeof EPR chart right in front of me that belongs to an IAE V2500 engine. This table says that for a specific temperature, Takeoff EPR is greater the higher the airplane is. As an example, 15 Celcius at sea level gives me 1.397 whereas 15 Celcius at 8000 feet gives me 1.587.

I also don't understand why the engine looses thrust when the bleeds are on.
Thanks for your help.

[FE Hoppy]

EPR
Engine Pressure Ratio

Pressure out / Pressure in


Thrust

Mass x velocity

With lower pressure going in you need a higher ratio to achieve the same thrust.

[barit1]

The "bleeds on" situation is this: Taking bleed air away from the compressor means less air is available to turn the turbine, so the fuel/air ratio gets a little richer as the FCU (or FADEC) tries to maintain engine RPM or EPR.

This results in higher EGT, not healthy for longevity of the hot parts.

So the engine power management calls for a decrement in EPR (or N1) to try to keep EGT back to original level. Thus thrust is a bit reduced for bleeds on.