LinProg(f, AInEq, bInEq, AEq, bEq, debug)

Solves Linear Programming poblem

% x = LinProg(f, AInEq, bInEq)

% x = LinProg(f, AInEq, bInEq,AEq, bEq)

% x = LinProg(f, AInEq, bInEq,AEq, bEq,debug)

% [x,fval] = LinProg(___)

% [x,fval,exitflag] = LinProg(___)

%This function implments the simplex matrix algorithm.

%It accepts row vector f defining the objective function as f*x

%It can accept only inequality constraints(as in x = LinProg(f, AInEq, bInEq)) ,

% or only equality constraints (as in x = LinProg(f, [], [], AEq, bEq).

% The debug defaults false if the use did not specify to see the stages

% during the solution process

%

%It runs both phase one and phase two automatically.

%

%The input is

%

%AInEq and bInEq: defined the inequality constrain AInEq*x <= bInEq

%

%AEq and bEq: defined the equality constrain AEq*x = bEq

%

%f: Vector. This is from minimize F(x) = fx. As defined in

% standard Matlab documentations.

%

%debug: flag. Set to true to see lots of internal steps.

%

% Version 7/16/2017( modification of original version by Nasser M. Abbasi)

% by Lateef A. Kareem

% Free for use.