LinearProgramming

Minimize , subject to constraint and lower bounds , :

Minimize , subject to constraint and bounds , :

Minimize , subject to constraint and upper bounds , :

Minimize , subject to constraint and implicit non-negative constraints:

Minimize subject to bounds and only:

Solve the same kind of problem, but with both variables integers:

Solve the same problem, but with the first variable an integer:

Solve larger LPs, in this case 200,000 variables and 10,000 constraints:

Objective, constraints, and bounds can all be specified as SparseArray:

is faster than or , though it only works for machine-precision problems:

If an approximated solution is sufficient, a loose Tolerance option makes the solution process faster:

A linear programming problem can also be solved using Minimize:

NMinimize or FindMinimum can be used to solve inexact linear programming problems:

The integer programming algorithm is limited to the machine-number problems:

The method only works for machine numbers:

The method may return a solution in the middle of the optimal solution set:

The method always returns a solution at a corner of the optimal solution set:

In this case the optimal solution set is the set of all points on the line segment between and :

The method may not always be able to tell if a problem is infeasible or unbounded:

This expresses the Klee-Minty problem of dimension in LinearProgramming syntax:

Because scaling is applied internally, the simplex algorithm converges very quickly: