Introduction to Linear Programming

Fundamental Theorem of Linear Programming

Steps to Solve LP Problems

1. Define variables
2. Write the objective function
3. Write constraints
4. Graph the feasible region
5. Find corner points
6. Evaluate objective function at each corner point
7. Compare values to find optimum

Example: Formulate LP Problem

A furniture maker produces tables and chairs. Each table requires 2 hours of carpentry and 1 hour of finishing. Each chair requires 1 hour of carpentry and 1 hour of finishing. There are 100 hours of carpentry and 80 hours of finishing available. Profit per table is ₹500 and per chair is ₹300. Formulate as LP problem.

Types of Solutions

Example: Check Feasibility

Check if the following constraints define a non-empty feasible region: , ,