In[]:=
Reduce-2*a1x+10(a1x+a1y-10)+g10&&-2*a1y+10(a1x+a1y-10)+g2==0&&0.9*(-2*a2x*(1-ix/40)+10/(a2x+a2y-10))+g3==0&&0.9*(-2*a2y*(1-ix/40)+10/(a2x+a2y-10))+g4==0&&-0.5+0.9*
2
a2x
40+
2
a2y
40+g5==0&&-0.5+g60&&g1*(-a1x)0&&g2*(-a1y)0&&g3*(-a2x)0&&g4*(-a2y)0&&g5*(-ix)0&&g6*(-iy)0&&g7*(ix-24)0&&g8*(iy-24)0&&a1x>=0&&a1y>=0&&a2x>=0&&a2y>=0&&ix>=0&&iy>=0&&ix≤24&&iy≤24&&g1≥0&&g2≥0&&g3≥0&&g4≥0&&g5≥0&&g6>=0&&g7>=0&&g8≥0,{a1x,a1y,a2x,a2y,ix,iy,g1,g2,g3,g4,g5,g6,g7,g8}
Reduce
:Reduce was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result.
Out[]=
(a1x0&&a1y0&&a2x0&&a2y0&&ix0&&iy0&&g11.&&g21.&&g30.9&&g40.9&&g50.5&&g60.5&&g70&&g80)||(a1x5.45804&&a1y5.45804&&a2x0&&a2y0&&ix0&&iy0&&g10&&g20&&g30.9&&g40.9&&g50.5&&g60.5&&g70&&g80)