clear all;
close all;

%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% PROBLEMA 1
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Ricordare ilsignificato di exitflag:
%      1  LINPROG converged to a solution X.
%      0  Maximum number of iterations reached.
%     -2  No feasible point found.
%     -3  Problem is unbounded.
%     -4  NaN value encountered during execution of algorithm.
%     -5  Both primal and dual problems are infeasible.
%     -7  Search direction became too small; no further progress can be made. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Definizione problema
%% f = -x1 + x2
%% x1-2*x2>=2
%% x1+x2<=4
%% x1<=3
%% xi>=0, i=1,2
%%%%%%%%%%%%%%%%%%%%%%%%%%%
fun = [-1 1]';
A = [-1 2;
    1   1;
    1   0];
b = [-2 4 3]';
lb = zeros(2,1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% linprog usato con la
%% sintassi classica
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
options=optimset('LargeScale','off','Display','iter','Simplex','on');
[x,fval,exitflag,output,lambda] = linprog(fun,A,b,[],[],lb,[],[],options)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% linprog con struttura
%% di input
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
problema1 = struct('f',fun,'Aineq',A,'bineq',b,'Aeq',[],'beq',[],...
    'x0',[],'lb',lb,'ub',[],'options',options,'solver','linprog')
[x,fval,exitflag,output,lambda] = linprog(problema1)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Rappresentazione grafica
%% del problema
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
a1=0; b1=6;
a2=-3; b2=3;
x1 = linspace(a1,b1,20);
x2 = linspace(a2,b2,20);
[X1,X2]=meshgrid(x1,x2);
Y = -X1+X2;

figure(1);
hold on
[c,h]=contour(X1,X2,Y,[-5 -4 -3 -2 -1 0]);
clabel(c,h);
line([0 0],[a2 b2],'Color','k','LineStyle',':')
line([0 6],[0 0],'Color','k','LineStyle',':')
line([3 3],[a2 b2],'Color','k','LineStyle',':')
plot(x1,x1/2-1,'k:')
x3 = linspace(1,6,20);
plot(x3,4-x3,'k:')
fill([2 3 3],[0 1/2 0],[1 0 0])
xlabel('X1')
ylabel('X2')
axis equal
hold off



%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% PROBLEMA 2
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Definizione problema
%% f = 2*x1 + 4*x2 + 3*x3
%% -x1+x2+x3>=2
%% 2*x1+x2>=1
%% xi>=0, i=1,2,3
%%%%%%%%%%%%%%%%%%%%%%%%%%%
fun = [2 4 3]';
A = [1 -1 -1;
    -2 -1  0];
b = [-2 -1]';
lb = zeros(3,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% linprog con struttura
%% di input
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
problema2 = struct('f',fun,'Aineq',A,'bineq',b,'Aeq',[],'beq',[],...
    'x0',[],'lb',lb,'ub',[],'options',options,'solver','linprog')
[x,fval,exitflag,output,lambda] = linprog(problema2)



%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% PROBLEMA 3
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Definizione problema
%% f = -3/4*x1 + 20*x2 - 1/3*x3 + 6*x4
%% 1/4*x1-8*x2-x3+9*x4<=1
%% 1/2*x1-12*x2-1/2*x3+3*x4<=3
%% x3+x4<=1
%%%%%%%%%%%%%%%%%%%%%%%%%%%
fun = [-3/4 20 -1/2 6]';
A = [1/4 -8  -1   9;
     1/2 -12 -1/2 3;
     0    0   1   1];
b = [1 3 1]';
lb = zeros(4,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% linprog con struttura
%% di input
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
problema3 = struct('f',fun,'Aineq',A,'bineq',b,'Aeq',[],'beq',[],...
    'x0',[],'lb',lb,'ub',[],'options',options,'solver','linprog')
[x,fval,exitflag,output,lambda] = linprog(problema3)



%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% PROBLEMA 4
%% Con soluzioni multiple
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Definizione problema
%% f = -x1 -x2
%% x1-x2<=1
%% x1+x2<=2
%%%%%%%%%%%%%%%%%%%%%%%%%%%
fun = [-1 -1]';
A = [1 -1;
     1  1];
b = [1 2]';
lb = zeros(2,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% linprog con struttura
%% di input
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
problema4 = struct('f',fun,'Aineq',A,'bineq',b,'Aeq',[],'beq',[],...
    'x0',[],'lb',lb,'ub',[],'options',options,'solver','linprog')
[x,fval,exitflag,output,lambda] = linprog(problema4)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Rappresentazione grafica
%% del problema
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
a1=0; b1=6;
a2=-3; b2=3;
x1 = linspace(a1,b1,20);
x2 = linspace(a2,b2,20);
[X1,X2]=meshgrid(x1,x2);
Y = -X1-X2;

figure(2);
hold on
[c,h]=contour(X1,X2,Y,[-5 -4 -3 -2 -1 0]);
clabel(c,h);
line([0 0],[a2 b2],'Color','k','LineStyle',':')
line([0 6],[0 0],'Color','k','LineStyle',':')
plot(x1,x1-1,'k:')
plot(x1,2-x1,'k:')
%fill([1 3/2 2],[0 1/2 0],[1 0 0])
f1=fill([0 0 5],[-3 2 -3],[1 .7 .7],'FaceAlpha',.5)
f2=fill([0 0 4 6 6],[-3 -1 3 3 -3],[.7 1 .7],'FaceAlpha',.5)
f3=fill([0 0 6 6],[0 3 3 0],[.7 .7 1],'FaceAlpha',.5)
xlabel('X1')
ylabel('X2')
axis equal
hold off