optimize with linear constraints and bounds in matlab

In MATLAB, you can use the linprog function to optimize a linear programming problem with linear constraints and bounds.

The linprog function requires the following inputs:

• Objective function coefficients: Specify the coefficients of your objective function as a row vector.
• Inequality constraint matrix: Specify the inequality constraints as A, where A*x <= b.
• Inequality constraint right-hand side: Specify the right-hand side values of the inequality constraints as a column vector b.
• Equality constraint matrix: Specify the equality constraints as Aeq, where Aeq*x = beq.
• Equality constraint right-hand side: Specify the right-hand side values of the equality constraints as a column vector beq.
• Variable bounds: Specify the lower and upper bounds for the variables as lb and ub, respectively. The variable bounds should be specified as vectors of the same length as the number of variables.

Here's an example that demonstrates how to use the linprog function to optimize a linear programming problem with linear constraints and bounds:

main.m
% Objective function coefficients
f = [2; 3];

% Inequality constraint matrix
A = [1 1; -1 2; 3 2];

% Inequality constraint right-hand side
b = [4; 3; 7];

% Equality constraint matrix
Aeq = [1 -1];

% Equality constraint right-hand side
beq = 2;

% Variable bounds
lb = [0; 0];
ub = [Inf; Inf];

% Solve the linear programming problem
[x, fval] = linprog(f, A, b, Aeq, beq, lb, ub);

% Display the optimal solution and objective function value
disp('Optimal Solution:');
disp(x);
disp('Objective Function Value:');
disp(fval);
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