Linear Programming (LP)

A mathematical technique to allocate limited resources in an optimal way.

Problem Formulation

Every LP problem has three components:

  1. Decision Variables: What we want to decide (e.g., $x_1$ = units of Product A).
  2. Objective Function: What we want to maximize or minimize (e.g., Max $Z = 50x_1 + 40x_2$).
  3. Constraints: Limitations (e.g., $2x_1 + 3x_2 \le 100$ hours).

Graphical Method

Used for 2 variables. We plot the constraints on a graph to find the Feasible Region.

The optimal solution always lies at a Corner Point of the feasible region.

Simplex Method

An algebraic algorithm used for solving LP problems with more than 2 variables. It moves from one corner point to another until the best one is found.

Test Yourself

Q1: In the graphical method, the optimal solution is always found at:

  • The center of the region
  • A corner point
  • The origin