ineq1=8x1+5x2≥ 80
ineq2=6x1+4x2≥60 
ineq3=4x1+4x2≥50
Show[RegionPlot[ineq1,{x1,0,20},{x2,0,20}],RegionPlot[ineq2,{x1,0,20},{x2,0,20}],RegionPlot[ineq3,{x1,0,20},{x2,0,20}]]

Manipulate[Show[RegionPlot[ineq1 && ineq3,{x1,0,20},{x2,0,20}],ContourPlot[-100x1-60x2==g,{x1,0,20},{x2,0,20}]],{g,-2000,-900,10}]

Solve[{8x1+5x2== 80,4x1+4x2==50},{x1,x2}]

g[p1_,p2_]:=100p1+60p2

g[12.5,0]
g[35/6,20/3.0]
g[0,16]

Solve[80x+60y+50z==960,z]

z=-(2/5) (-48+4 x+3 y)
ineq1=Simplify[8x+6y+4z≤100]
ineq2=Simplify[5x+4y+4z≤60]
ineq3=Simplify[z≥0]

Show[RegionPlot[ineq1,{x,0,20},{y,0,20}],RegionPlot[ineq2,{x,0,20},{y,0,20}],RegionPlot[ineq3,{x,0,20},{y,0,20}]]

Solve[{4 x+3 y==48,7 x+4 y==84},{x,y}]

80 12