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Linear Programming

  • Problems which seek to maximise (or minimise) a function subject to certain constraints are called optimisation problems.
  • A Linear Programming Problem (L.P.P.) is the one that is concerned with finding the optimal value (maximum or minimum value) of a linear function of several variables (called objective function), subject to the conditions that the variables are non-negative and satisfy a set of linear inequalities (called constraints). The variables are sometimes called the decision variables.

For example: The following is an L.P.P.

Maximize Z = 10x + 12y

Subject to the following constraints:

5x + 3y ≤ 30                            ... (1)

x + 2y 2                                ... (2)

x 0, y 0                              ... (3)

In this L.P.P, the objective function is Z = 10x + 12y

The inequalities (1), (2), and (3) are called constraints.

  • The common regio‚Ķ

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