Objective Function in Linear Programming

Introduction to Objective Functions

• Objective Function: A mathematical expression that describes a quantity to be maximized or minimized.
• Commonly used in linear programming, a method for solving optimization problems.
• Widely applied in management science to optimize resources and outcomes.

Applications of Objective Functions

• Business: Maximizing profit is a typical goal.
• Humanitarian Aid: In scenarios like shipping bottled water and medical kits to earthquake survivors, the objective is to maximize the number of survivors helped.

Example Problem: Aid Shipment

• Scenario: Bottled water and medical supplies to be shipped by plane to earthquake survivors.
  • Bottled Water: Each container serves 10 people.
  • Medical Kits: Each kit aids 6 people.

Variables

• x: Number of bottled water containers to be shipped.
• y: Number of medical kits to be shipped.

Objective Function

• Objective: Maximize the number of people helped.
• Expression:
  • Let z be the total number of people helped.
  • Objective function: z = 10x + 6y
  • 10x: Represents the people served by bottled water.
  • 6y: Represents the people aided by medical kits.

Conclusion

• Writing an objective function involves expressing the goal of maximizing or minimizing a specific outcome, using the given variables and constraints.
• Objective functions are critical in resource allocation and optimizing processes in various fields.