% Define the objective function coefficients (excluding the constant)
f_coeffs = [-0.05, -0.04];
% Define the inequality constraints (A*x <= b)
A = [1, 1; % y <= -x + 12 => x + y <= 12
-1, -1; % y >= -x + 10 => -x - y <= -10
-1, 3]; % y <= (1/3)x => -x + 3y <= 0
b = [12, -10, 0];
% Define the lower bounds for x and y (x >= 0, y >= 0)
lb = [0, 0];
% Solve the linear programming problem
[x, fval] = linprog(f_coeffs, A, b, [], [], lb);
% Calculate the actual objective function value (including the constant)
f_actual = 1.44 + fval;
% Display the results
fprintf('Optimal solution:\n');
fprintf('x = %.4f\n', x(1));
fprintf('y = %.4f\n', x(2));
fprintf('Objective function value = %.4f\n', f_actual);
% Plotting the feasible region and optimal solution
% 1. Define the line for the constraints
x_plot = 0:15; % Set the range for x
y1 = -x_plot + 12;
y2 = -x_plot + 10;
y3 = (1/3) * x_plot;
% 2. Plot the lines
figure;
plot(x_plot, y1, 'r-', 'DisplayName', 'y <= -x + 12');
hold on;
plot(x_plot, y2, 'b-', 'DisplayName', 'y >= -x + 10');
plot(x_plot, y3, 'g-', 'DisplayName', 'y <= (1/3)x');
% 3. Fill the feasible region
x_fill = [0, 6, 12, 10,0];
y_fill = [0, 2, 0, 0, 10];
fill(x_fill,y_fill,'y','FaceAlpha',0.3,'DisplayName','Feasible Region');
% 4. Plot the optimal point
plot(x(1), x(2), 'ko', 'MarkerSize', 8, 'MarkerFaceColor', 'k', 'DisplayName', 'Optimal Point');
% 5. Add labels and legend
xlabel('x');
ylabel('y');
title('Feasible Region and Optimal Solution');
legend('show');
grid on;
axis([0, 15, 0, 15]); % Adjust axis limits as needed
hold off;
