%% Examine the MILP Solution and Process
% Call intlinprog with more outputs to see solution details and process.
% The goal is to solve the problem
%  \mathop {\min }\limits_x \left( { - 3{x_1} - 2{x_2} - {x_3}} \right)
% {\rm{\ subject\ to }}\left\{ {\begin{array}{*{20}{l}}
% {{x_3}{\rm{\ binary}}}\\
% {{x_1},{x_2} \ge 0}\\
% {{x_1} + {x_2} + {x_3} \le 7}\\
% {4{x_1} + 2{x_2} + {x_3} = 12.}
% \end{array}} \right.
%
% Specify the solver inputs.

f = [-3;-2;-1];
intcon = 3;
A = [1,1,1];
b = 7;
Aeq = [4,2,1];
beq = 12;
lb = zeros(3,1);
ub = [Inf;Inf;1]; % enforces x(3) is binary

%
% Call intlinprog with all outputs.

[x,fval,exitflag,output] = intlinprog(f,intcon,A,b,Aeq,beq,lb,ub)

% The output structure shows numnodes is 0. This means intlinprog solved the problem before branching. This is one indication that the result is reliable. Also, the absolutegap and relativegap fields are 0. This is another indication that the result is reliable.
% Copyright 2012 The MathWorks, Inc.