let {i in A} a[i] := 0;
let a[1] := -100;
let a[2] :=  200;
let a[3] := -100;

let {i in N} l[i] := 2;

let {i in N} c[i] := ((1-beta)/(alpha*beta))*(K[i]^alpha)*(l[i]^(1-alpha));

option filter_options "maxiter=20000";
option ipopt_options 'iprint=0 imaxiter=20000 dtol=1e-6';
option snopt_options "iterations_limit=500000 Major_iterations= 50000";

solve;

display a;
display {i in N} (K[i], c[i], l[i], util[i], sum {j in A} a[j]*K[i]^(j-1), sum {j in A} a[j]*(F[i]-c[i])^(j-1), Vgrad.body[i], Vhess.body[i], BellmanEQ.body[i]);

display _solve_time ;