Operations research

1. Linear Programming in
Operations Research
For B.Sc. Mathematics | 6th
Semester
Prepared by: [Your Name]

2. Introduction to Linear
Programming
• • Mathematical method for optimization.
• • Maximizes or minimizes an objective
function.
• • Subject to constraints and non-negativity
conditions.

3. Formulation of Linear
Programming Problems
• 1. Identify decision variables.
• 2. Define the objective function.
• 3. Establish constraints.
• 4. Ensure non-negative conditions.

4. Graphical Method
• • Used for two-variable problems.
• • Plot constraints as lines on a graph.
• • Identify feasible region and optimal point.

5. Simplex Method
• • Used for multi-variable problems.
• • Iterative process to find optimal solution.
• • Involves pivot operations in a tabular format.

6. Duality in Linear Programming
• • Every LP problem has a dual problem.
• • The solution of one provides insights into
the other.
• • Helps in economic interpretation and
sensitivity analysis.

7. Applications of Linear
Programming
• • Resource allocation
• • Transportation and logistics
• • Production planning
• • Financial optimization
• • Workforce scheduling

8. Advantages and Limitations
• Advantages:
• • Provides optimal solutions.
• • Handles multiple constraints.
• • Aids decision-making.
• Limitations:
• • Assumes linear relationships.
• • Cannot handle uncertainty directly.
• • Complex for large problems.

9. Case Study: Manufacturing
Optimization
• • A factory produces two products: A and B.
• • Objective: Maximize profit.
• • Constraints: Limited raw materials and labor.
• • Solution: Use LP to find the optimal
production mix.

10. Conclusion
• • Linear Programming is crucial in Operations
Research.
• • Helps in optimizing resources effectively.
• • Understanding different methods enhances
problem-solving skills.