Clear["Global`*"]
LIV=Pi/2(D1-d D1+2dDf)+λ(d Pi/4(2D1+2D2+4Df-D1^2-D2^2-4Df^2-2)-Pon)+μ1(-D1/2-D2/2+Df)+μ2(1-D1/2-D2/2-Df)+μ3(D1-1)+μ4(D2-1)
solutionsIV=Solve[{D[LIV,D1]==0,D[LIV,D2]==0,D[LIV,Df]==0,dPi/4(2D1+2D2+4Df-D1^2-D2^2-4Df^2-2)-Pon==0,μ1(-D1/2-D2/2+Df)==0,μ2(1-D1/2-D2/2-Df)==0,μ3(D1-1)==0,μ4(D2-1)==0,μ1>=0,μ2>=0,μ3>=0,μ4>=0,-D1/2-D2/2+Df<=0,1-D1/2-D2/2-Df<=0,D1-1<=0,D2-1<=0,0<d<1,Pon>0},{D1,D2,Df,λ,μ1,μ2,μ3,μ4},Reals]//Simplify

写法没啥问题，只是就是要这么久罢了吧。
去掉Simplify改用Reduce倒是挺快