Linear programming

Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical mode whose requirements are represented by linear relationships.

More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear inequality constraints.

There are two types:
 
– maximize the objective function

     z = c1x1 + c2x2 +….+ cnxn

     with the constraints:

 

– minimize the objective function

    z = c1x1 + c2x2 +….+ cnxn  

    with the constraints:

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