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* = 10*x* + 12*y*

Subject to the following constraints:

5*x* + 3*y* ≤ 30 ... (1)

*x* + 2*y* ≥ 2 ... (2)

*x* ≥ 0, *y *≥ 0 ... (3)

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

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

- The common regio…

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