# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# LinearProgramming

LinearProgramming[c,m,b]
finds a vector x that minimizes the quantity c.x subject to the constraints m.xb and x0.

LinearProgramming[c,m,{{b1,s1},{b2,s2},}]
finds a vector x that minimizes c.x subject to x0 and linear constraints specified by the matrix m and the pairs {bi,si}. For each row mi of m, the corresponding constraint is mi.xbi if si==1, or mi.x==bi if si==0, or mi.xbi if si==-1.

LinearProgramming[c,m,b,l]
minimizes c.x subject to the constraints specified by m and b and xl.

LinearProgramming[c,m,b,{l1,l2,}]
minimizes c.x subject to the constraints specified by m and b and xili.

LinearProgramming[c,m,b,{{l1,u1},{l2,u2},}]
minimizes c.x subject to the constraints specified by m and b and lixiui.

LinearProgramming[c,m,b,lu,dom]
takes the elements of x to be in the domain dom, either Reals or Integers.

LinearProgramming[c,m,b,lu,{dom1,dom2,}]
takes xi to be in the domain domi.

## Details and OptionsDetails and Options

• All entries in the vectors c and b and the matrix m must be real numbers.
• The bounds li and ui must be real numbers or Infinity or .
• None is equivalent to specifying no bounds.
• LinearProgramming gives exact rational number or integer results if its input consists of exact rational numbers.
• LinearProgramming returns unevaluated if no solution can be found.
• LinearProgramming finds approximate numerical results if its input contains approximate numbers. The option Tolerance specifies the tolerance to be used for internal comparisons. The default is , which does exact comparisons for exact numbers, and uses tolerance for approximate numbers.
• SparseArray objects can be used in LinearProgramming.
• With Method->"InteriorPoint", LinearProgramming uses interior point methods.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

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

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Solve the problem with equality constraint and implicit non-negative constraints:

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Solve the problem with equality constraint and implicit non-negative constraints:

 In[3]:=
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