# Documentation

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## Typical Linear Programming Problem

This example shows the solution of a typical linear programming problem. The problem is

You can load the matrices and vectors `A`, `Aeq`, `b`, `beq`, `f`, and the lower bounds `lb` into the MATLAB® workspace with

`load sc50b`

The problem in `sc50b.mat` has 48 variables, 30 inequalities, and 20 equalities.

Use `linprog` to solve the problem:

```options = optimoptions(@linprog,'Algorithm','dual-simplex','Display','iter'); [x,fval,exitflag,output] = ... linprog(f,A,b,Aeq,beq,lb,[],options);```

Because the iterative display was set using `optimoptions`, the results displayed are

```LP preprocessing removed 2 inequalities, 16 equalities, 16 variables, and 26 non-zero elements. Iter Time Fval Primal Infeas Dual Infeas 0 0.001 0.000000e+00 0.000000e+00 1.305023e+00 6 0.001 -1.587098e+02 4.008882e+02 0.000000e+00 33 0.002 -7.000000e+01 0.000000e+00 0.000000e+00 Optimal solution found.```

The `exitflag` value is positive, telling you `linprog` converged. You can also get the final function value in `fval` and the number of iterations in `output.iterations`:

```exitflag,fval,output exitflag = 1 fval = -70 output = struct with fields: iterations: 33 constrviolation: 3.4106e-13 message: 'Optimal solution found.' algorithm: 'dual-simplex' firstorderopt: 2.5180e-14```