BUILT-IN MATHEMATICA SYMBOL

# LinearProgramming

LinearProgramming[c, m, b]
finds a vector x that minimizes the quantity subject to the constraints and x≥0.

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

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

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

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

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 to be in the domain .

## Details and OptionsDetails and Options

• All entries in the vectors c and b and the matrix m must be real numbers.
• The bounds and 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:

 Out[1]=

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

 Out[2]=

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

 Out[3]=