restart; eq1 := (P[A]*(p-w)/(1-P[A])-c)*H[A]+(w-P[A]*(p-w)/(1-P[A]))*P[A]*H[A]+w[u]*P[B]*(1-P[A])*H[B] < (P[B]*(p-w)/(1-P[B])-c)*H[B]+(w-P[B]*(p-w)/(1-P[B]))*P[B]*H[B]+w[u]*P[A]*(1-P[B])*H[B]; eqn2 := expand(simplify(collect(eq1, H[A]))); eqn3 := algsubs(H[B]*P[A]*P[B]*w[u] = x, eqn2); eqn4 := collect(collect(collect(lhs(eqn3)-rhs(eqn3) < 0, c), w[u]), p); op([1, 1], eqn4)+collect(op([1, 2], eqn4), H[B])+op([1, 3], eqn4) < 0; op([1, 1], eqn4);
restart:
eq1:=(P[A]*(p-w)/(1-P[A])-c)*H[A]+(w-P[A]*(p-w)/(1-P[A]))*P[A]*H[A]+w[u]*P[B]*(1-P[A])*H[B] < (P[B]*(p-w)/(1-P[B])-c)*H[B]+(w-P[B]*(p-w)/(1-P[B]))*P[B]*H[B]+w[u]*P[A]*(1-P[B])*H[B];
eqn2:=expand(simplify(collect(eq1, H[A])));
eqn3:=algsubs(H[B]*P[A]*P[B]*w[u]=x,eqn2);
eqn4:=collect(collect(collect(lhs(eqn3)-rhs(eqn3)<0,c), w[u]),p);
op([1,1], eqn4)+collect(op([1,2],eqn4), H[B])+op([1,3], eqn4)<0;
op([1,1], eqn4);
