[Optimization] For matlab and cvx

let's consider a simple linear programming problem using MATLAB and the CVX toolbox. In this example, we want to maximize the objective function f(x,y)=3x+2yf(x,y)=3x+2y subject to the constraints:

2x+y≤20

2x+y≤20 4x−5y≥−10

4x−5y≥−10 x,y≥0 x,y≥0

Here's how you can use MATLAB with CVX to solve this optimization problem:

% Install CVX (if not installed) and add to the MATLAB path
% (Make sure you have a working internet connection for installation)
% cvx_setup;

% Define the decision variables
cvx_begin
    variables x y
    
    % Define the objective function to maximize
    maximize(3*x + 2*y)
    
    % Subject to constraints
    subject to
        2*x + y <= 20
        4*x - 5*y >= -10
        x >= 0
        y >= 0
cvx_end

% Display the results
fprintf('Optimal value of x: %.2f\n', x);
fprintf('Optimal value of y: %.2f\n', y);
fprintf('Optimal objective function value: %.2f\n', 3*x + 2*y);