% Sensitivity analysis
% We consider the problem given in Kartik's lecture notes on sensitivity analysis
% Kartik's MATLAB session
% To try out the session type the following commands (in that order!)
clear all;
c=[5 1 -12 0]';
A=[3 2 1 0; 5 3 0 1];
b=[10 16]';
eps = 1e-6;
B=[3 4];
[obj,x,y] = revised_simplex(c,A,b,eps,B);
% Optimal solution is
% x= [2 2 0 0], y=[-10 7] for a objective value of 12

% Case a) Adding a new column
A1 = [A [1 1]'];
c1 = [c; 1];
B1 = [1 2];
% We can reoptimize with the revised simplex method
[obj1,x1,y1] = revised_simplex(c1,A1,b,eps,B1);
% Optimal solution is
% x = [3 0 0 0 1], y=[0 1] for a objective value of 16


% Case b) Adding a new inequality constraint
A2 = [A zeros(2,1); 1 1 0 0 -1];
c2 = [c; 0];
b2 = [b; 5];
% We will reoptimize with the dual simplex method
x0 = [2 2 0 0 -1]';
x2 = dual_simplex(c2,A2,b2,eps,x0);
% Optimal solution is
% x = [0 5 0 1 0] for a objective value of 5

% Case c) Changes to the rhs vector b
b3 = [11 16]';
x0 = [-1 7 0 0]';
% We will reoptimize with the dual simplex method
x3 = dual_simplex(c,A,b3,eps,x0);
% Optimal solution is
% x = [0 5.33 0.33 0] for a objective value of 1.33

% Case d) Changes in c_N
c4 = [5 1 -9 0]';
B4 = [1 2];
% We will reoptimize with the primal simplex method
[obj,x4,y4] = revised_simplex(c4,A,b,eps,B4);
% Optimal solution is
% x = [3.2 0 0.4 0], y = [-9 6.4] for a objective value of 12.4