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    %% 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.