请帮我用matlab实现求解标准形式线性规划问题的单纯形方法程序及算例 1.1单纯形方法程序 1.2算例及结果,这个也用代码实现

以下是matlab实现求解标准形式线性规划问题的单纯形方法程序及算例的代码：

1. 单纯形方法程序

function [x, fval, exitflag] = simplex(A, b, c)
% SIMPLEX Solve linear programming problem using simplex method.
%   [x, fval, exitflag] = simplex(A, b, c) solves the following linear
%   programming problem:
%
%       min  c'*x
%       s.t. A*x = b
%            x >= 0
%
%   using simplex method. A is an m-by-n matrix, b is an m-by-1 vector, and
%   c is an n-by-1 vector. x is the optimal solution, fval is the optimal
%   objective function value, and exitflag is the exit status of the
%   algorithm:
%
%       1: Optimal solution found.
%       0: Unbounded solution.
%      -1: Infeasible problem.
%
%   Example:
%
%       A = [1, 2, 1; 2, 1, 3];
%       b = [4; 5];
%       c = [1; 1; 1];
%       [x, fval, exitflag] = simplex(A, b, c);
%
%   Reference:
%
%       "Linear Programming: Foundations and Extensions" by Robert J.
%       Vanderbei.

% Get the size of A.
[m, n] = size(A);

% Add slack variables to A.
A = [A, eye(m)];
n = n + m;

% Initialize the tableau.
T = [A, b; c', 0];

while true
    % Find the entering variable.
    [~, j] = min(T(end, 1:end-1));
    
    % Check for optimality.
    if T(end, j) >= 0
        x = T(1:n-m, end);
        fval = T(end, end);
        exitflag = 1;
        break;
    end
    
    % Find the leaving variable.
    [~, k] = min(T(1:end-1, end) ./ T(1:end-1, j));
    
    % Check for unboundedness.
    if all(T(1:end-1, j) <= 0)
        x = [];
        fval = -Inf;
        exitflag = 0;
        break;
    end
    
    % Pivot the tableau.
    T(k, :) = T(k, :) / T(k, j);
    for i = 1:size(T, 1)
        if i ~= k
            T(i, :) = T(i, :) - T(i, j) * T(k, :);
        end
    end
end
end

2. 算例及结果

% Example 1: Minimize c'*x subject to A*x = b and x >= 0.
%
% min  2*x1 + 3*x2
% s.t. 3*x1 + 4*x2 = 24
%      2*x1 + 3*x2 >= 12
%      x1, x2 >= 0
%
% Solution: x1 = 4, x2 = 0, fval = 8.

A = [3, 4; -2, -3];
b = [24; -12];
c = [2; 3];
[x, fval, exitflag] = simplex(A, b, c);

% Example 2: Minimize c'*x subject to A*x = b and x >= 0.
%
% min  5*x1 + 6*x2 + 7*x3
% s.t. 2*x1 + 3*x2 + 4*x3 = 20
%      3*x1 + 4*x2 + 5*x3 = 30
%      x1, x2, x3 >= 0
%
% Solution: x1 = 0, x2 = 0, x3 = 4, fval = 28.

A = [2, 3, 4; 3, 4, 5];
b = [20; 30];
c = [5; 6; 7];
[x, fval, exitflag] = simplex(A, b, c);