NMinimize[{3/X1+4/X2,{0≤X1≤1,0≤X2≤1,Sqrt[3]*X1+4/Sqrt[3]*X2≤1}},{X1,X2}]

Solve[3/X1+4/X2==28.2902,X1]

Solve[Sqrt[3]*X1+4/Sqrt[3]*X2==1,X1]

g1=((15000.` X2)/(-20000.`+141451.` X2))
g2=-((-3+4 (Sqrt[3]) X2)/(3 (Sqrt[3])))

Plot[{g1,g2},{X2,0.15,0.5},PlotRange->{{0.15,0.5},{0.15,0.5}}]