[ \textAP \textper day = f^-1\left( \fracR \texttarget3 \right) ]

Then apply and global activity coefficient ( G ) (Gaijin’s hidden server-side multiplier, typically 1.0 except during events):

Solve ( \sum_d=1^3 f(\textAP d) = R \texttarget ) with constraint ( \textAP_d \le 3000 ) (practical limit). Assuming equal distribution for optimal time efficiency (proved via convexity of ( f )):

If ( y \le 360 ), ( x = y ). If ( 360 < y \le 540 ), ( x = 360 + (y - 360)/0.5 = 2y - 360 ). If ( 540 < y \le 696 ), ( x = 720 + (y - 540)/0.2 = 5y - 2700 ). If ( 696 < y \le 771 ), ( x = 1500 + (y - 696)/0.05 = 20y - 11400 ). If ( y > 771 ), impossible (daily cap).

[ \Delta_\textresearch = \frac\textFinal SP_\texttotal of all members \textVehicle cost in SP ]

Adjust for SEF: