On solving equations for variables included in functions R^n to R

*To*: mathgroup at smc.vnet.net*Subject*: [mg102375] On solving equations for variables included in functions R^n to R*From*: Mauricio Esteban Cuak <cuak2000 at gmail.com>*Date*: Fri, 7 Aug 2009 05:30:19 -0400 (EDT)

Hello. This question has to do half with mathematics and half with mathematica, so I apologise beforehand. I'm trying to symbollicaly maximize the following equation with respect to t1 and t2: obj = (1 - p1) (1 - p2)*U[ L[t1, t2] + iuno[t1, t2] + idos[t1, t2] ] + (1 - p1) (p2)*U[L[t1, t2] + iuno[t1, t2] + idos[t1, t2] - F ] + (p1) (1 - p2)*U[L[t1, t2] + iuno[t1, t2] + idos[t1, t2] - F ] + (p1)*(p2)*U[L[t1, t2] + iuno[t1, t2] + idos[t1, t2] - 2 F ]; As you can see, there are five undefined functions ( U, L, F, iuno, idos ), two parameters (p1, p2) and two variables (t1,t2). I know that the five functions have continuous and monotonic partial derivatives and that they are all concave. Given those assumptions, my first approach was to get the first-order conditions: eq1= Simplify [ D[obj,t1] ]; eq2 = Simplify [ D[obj,t2] ]; Which give the following output: eq1 = ( ((p1 - 1)*(p2 - 1)*Derivative[1][U][idos[t1, t2] + iuno[t1, t2] + L[t1, t2]] + p1*p2*Derivative[1][U][-2*F + idos[t1, t2] + iuno[t1, t2] + L[t1, t2]] + (-2*p2*p1 + p1 + p2)* Derivative[1][U][-F + idos[t1, t2] + iuno[t1, t2] + L[t1, t2]])* (Derivative[1, 0][idos][t1, t2] + Derivative[1, 0][iuno][t1, t2] + Derivative[1, 0][L][t1, t2]) == 0 ) and eq2 = ( ((-1 + p1)*(-1 + p2)*Derivative[1][U][idos[t1, t2] + iuno[t1, t2] + L[t1, t2]] + p1*p2*Derivative[1][U][-2*F + idos[t1, t2] + iuno[t1, t2] + L[t1, t2]] + (p1 + p2 - 2*p1*p2)* Derivative[1][U][-F + idos[t1, t2] + iuno[t1, t2] + L[t1, t2]])* (Derivative[0, 1][idos][t1, t2] + Derivative[0, 1][iuno][t1, t2] + Derivative[0, 1][L][t1, t2]) == 0 ) What I need now is to somehow solve the system of equations for t1 and t2, but as there are functions with two arguments, I don't know how to use inverse for them. Is there anyway to tell mathematica to construct a third function to express the inverse? If it can't be done, is there any way to obtain the symbolic maximum arguments t1 and t2? Thanks for your time! ep