% 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.
Lateef Adewale Kareem (2021). LinProg(f, AInEq, bInEq, AEq, bEq, debug) (https://www.mathworks.com/matlabcentral/fileexchange/63762-linprog-f-aineq-bineq-aeq-beq-debug), MATLAB Central File Exchange. Retrieved .
Inspired: Linear Programming Simplex Algorithm
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