Maximize several functions with constraints?

Questions
1

Hi all!
I’m new at Mathematica and I having the following problem. I define several functions to then optimize with constraints (complicated problem) using the function Maximize. The problem is that the output just prints the input, but gives no solutions to the problem. The problem has 16 constraints, 12 variables, and just one symbolic parameter.
If anyone can help with this I would really appreciate it. I post the code below.
Thanks!

uc[c_, delta_] := Times[delta, Divide[Power[c, -0.5], -0.5]]

vz[z_, w_] := Times[1, Divide[Power[Divide[z, w], 3], 3]]

ut[c1_, c2_, z_, w_, delta_] := uc[c1, 1] + uc[c2, delta] - vz[z, w]

SWF[c11_, c12_, c21_, c22_, c31_, c32_, c41_, c42_, z1_, z2_, z3_,z4_, w1_, w2_, delta_] := 
 ut[c11, c12, z1, w1, 1] + ut[c21, c22, z2, w1, delta] + ut[c31, c32, z3, w2, 1] + ut[c41, c42, z4, w2, delta]

mrs[c1_, c2_, delta_] :=  Times[Divide[1, delta], Power[Divide[c1, c2], -1.5]]

t[c1_, c2_] := Divide[1, mrs[c1, c2, 1]] - 1

R[c1_, c2_, c11_, c12_] := c1 + Times[(1 + t[c11, c12]), c2]

chat2[c1_, c2_, c11_, c12_, delta_] :=  Times[R[c1, c2, c11, c12], Power[Power[Divide[delta, 1 + t[c11, c12]], -Divide[2, 3]] + 1 + t[c11, c12], -1]]

chat1[c1_, c2_, c11_, c12_, delta_] := R[c1, c2, c11, c12] -   Times[(1 + t[c11, c12]), chat2[c1, c2, c11, c12, delta]]

ic[ci1_, ci2_, zi_, wi_, deltai_, cj1_, cj2_, zj_, c11_, c12_] := ut[ci1, ci2, zi, wi, deltai] - ut[chat1[cj1, cj2, c11, c12, deltai], chat2[cj1, cj2, c11, c12, deltai], zj, wi, deltai]

Maximize[{SWF[c11, c12, c21, c22, c31, c32, c41, c42, z1, z2, z3, z4, 
   1, 2, delta2], 
  c11 + c12 + c21 + c22 + c31 + c32 + c41 + c42 == z1 + z2 + z3 + z4 && 
   mrs[c11, c12, 1] == mrs[c21, c22, delta2] && 
   mrs[c11, c12, 1] == mrs[c31, c32, 1] && 
   mrs[c11, c12, 1] == mrs[c41, c42, delta2] && 
   ic[c11, c12, z1, 1, 1, c21, c22, z2, c11, c12] >= 0 && 
   ic[c11, c12, z1, 1, 1, c31, c32, z3, c11, c12] >= 0 && 
   ic[c11, c12, z1, 1, 1, c41, c42, z4, c11, c12] >= 0 && 
   ic[c21, c22, z2, 1, delta2, c11, c12, z1, c11, c12] >= 0 && 
   ic[c21, c22, z2, 1, delta2, c31, c32, z3, c11, c12] >= 0 && 
   ic[c21, c22, z2, 1, delta2, c41, c42, z4, c11, c12] >= 0 && 
   ic[c31, c32, z3, 2, 1, c11, c12, z1, c11, c12] >= 0 && 
   ic[c31, c32, z3, 2, 1, c21, c22, z2, c11, c12] >= 0 && 
   ic[c31, c32, z3, 2, 1, c41, c42, z4, c11, c12] >= 0 && 
   ic[c41, c42, z4, 2, delta2, c11, c12, z1, c11, c12] >= 0 && 
   ic[c41, c42, z4, 2, delta2, c21, c22, z2, c11, c12] >= 0 && 
   ic[c41, c42, z4, 2, delta2, c31, c32, z3, c11, c12] >= 0}, {c11, 
  c12, c21, c22, c31, c32, c41, c42, z1, z2, z3, z4}]
2

Maximize can’t handle problems with 12 variables and no parameters in any reasonable amount of time. However, the fact that it return the problem unevaluated probably means it wasn’t entered properly.