Interactive Linear Programming


Standard formulation of a linear program




Each problem in Linear Optimization can differ in terms of the objective function (the objective can be either to minimize or maximize a function), as well as in terms of the linear constraints (equality constraints, inequality constraints, smaller or equal, strictly smaller...). The Linear Program is then usually converted into its standard form.

The generic linear program is formulated as follows:


Minimize c1x1 + c2x2 +.....+ cnxn (Objective function)

Subject to:

1st constraint: a1,1x1+ a1,2x2+....+ a1,nxn+b1
2nd constraint:a2,1x1+ a2,2x2+....+ a2,nxn=b2
..................
..................
m-th constraint: am,1x1+ am,2x2+....+ am,nxn=bm
      
Positivity: x10 x20 ...xn 0 



Or, using vectors and matrices:

Min CX
Subject to:
where X0
and C such that

The problem is then to convert a general problem to a standard linear problem. Click here to know how to convert a general problem to a standard linear problem.
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