# Linear Programming

LP deals with the optimization of a function of variables known as *objective function/ cost function*, subject to a set of linear equations and/or inequalities called *constraints*.

#### Assumptions in LP

- Proportionality: some sort of proportionality exists between the objective function and constraints.
- Additivity:
- Continuity: decision variables can take any non-negative value that satisfies the constraints. However, some problems need integer values.
- Certainty: all LP problems are assumed to be
*deterministic*. - Finite Choices: a limited number of choices are available to the decision maker.

#### Formulation of LP problem.

**Step 1**: find the *key-decision* to be made by looking for variables.

**Step 2**: assume symbols for the variables and find the *extents* of variation.

**Step 3**: find *feasible alternatives* mathematically in terms of variables.

**Step 4**: mention the objective function *quantitavely*, as a linear function. Prepare a **cost function**.

**Step 5**: represent the *influencing factors* or **constraints** in mathematical terms.

#### Advantages of LP

- attain optimum use of productive factors
- improve quality of decisions
- can handle multiple constraints
- highlights the bottlenecks

#### Disadvantages of LP

- for large problems there are too many limitations and constraints, this makes the problem too difficult to solve even with computers
- the problems have to linearly approximated thus, the obtained results may be far from reality
- only
*static*situations can be dealt with - assume all values are known a priori with full certainty
- sometimes, the objective function and constraints cant be expressed in linear form
- multi-objective tasks cant be dealt with