Further Mathematics - Senior Secondary 1 - Models II - Practical Application of Models in Operations Research

Models II - Practical Application of Models in Operations Research

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TERM: 3RD TERM

WEEK 7
Class: Senior Secondary School 1
Age: 16 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Models II – Practical Application of Models in Operations Research
Focus: Applying Operations Research Models to Real-Life Problems

SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Understand the different types of models used in operations research (linear programming, transportation, etc.).
  2. Apply operations research models to solve practical problems.
  3. Use charts and graphical methods to present solutions to practical problems.
  4. Demonstrate problem-solving skills in a real-world context using the appropriate models.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Group work
  • Problem-solving practice
  • Discussion

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating the solution process of operations research problems
  • Graphing tools (optional)
  • Worksheets with sample operations research problems

PERIOD 1 & 2: Introduction to Models in Operations Research

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction to Models

Introduces the concept of operations research models, emphasizing the importance of applying mathematical models to real-world problems. Discusses types of models (linear programming, transportation models, etc.).

Students listen attentively, take notes, and ask clarifying questions.

Step 2 – Real-Life Applications

Explains how operations research models can solve practical issues like transportation optimization, resource allocation, and production scheduling.

Students observe examples and discuss real-life applications of the models.

Step 3 – Chart Demonstration

Uses charts to demonstrate how solutions are visualized in operations research (e.g., graphical method for linear programming problems).

Students follow the teacher’s demonstration and create similar charts in their notebooks.

NOTE ON BOARD: Operations Research Models:

  • Linear Programming: Maximize or minimize a linear objective function subject to constraints.
  • Transportation Problem: Minimize transportation cost while satisfying supply and demand constraints.
  • Other models (briefly mention).

EVALUATION (5 exercises):

  1. What is an operations research model?
  2. What types of problems can be solved using linear programming?
  3. Give an example of a real-life scenario where transportation models could be used.
  4. Explain the purpose of constraints in operations research models.
  5. Describe how graphs are used to solve problems in operations research.

CLASSWORK (5 questions):

  1. What are the two main goals of linear programming problems?
  2. Name one real-world application of operations research.
  3. How do you interpret the solution to a linear programming problem?
  4. In a transportation problem, what do supply and demand refer to?
  5. What does the graphical method help to solve in operations research?

ASSIGNMENT (5 tasks):

  1. Research an application of operations research in the industry.
  2. Create a simple transportation problem and solve it using a chart.
  3. Discuss how operations research can improve decision-making in business.
  4. Solve a basic linear programming problem with two variables.
  5. Write about the benefits of operations research in problem-solving.

 

PERIOD 3 & 4: Practical Application of Operations Research Models

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 – Guided Practice on Linear Programming

Demonstrates solving a linear programming problem graphically. Uses a real-world example (e.g., maximizing profit in a factory with constraints on resources).

Students observe the solution process, take notes, and ask questions.

Step 2 – Group Work on Practical Problems

Distributes worksheets with real-life problems that can be solved using operations research models. Guides students through the steps to solve each problem.

Students work in groups, discussing and solving the problems using the appropriate models.

Step 3 – Solution Presentation

Invites groups to present their solutions and the methods used. Provides feedback and additional tips for accuracy.

Students present their solutions, demonstrating the steps they followed and the model they used.

NOTE ON BOARD: Steps to Solve Linear Programming Problems:

  1. Define the decision variables.
  2. Write the objective function.
  3. List the constraints.
  4. Graph the constraints and find the feasible region.
  5. Determine the optimal solution from the graph.

EVALUATION (5 exercises):

  1. Solve the linear programming problem graphically: Maximize Z = 4x + 5y subject to the constraints x + y ≤ 8, 2x + y ≤ 10, x ≥ 0, y ≥ 0.
  2. Solve a transportation problem with the given supply and demand constraints.
  3. Find the optimal solution for a business using linear programming.
  4. Present an example of how operations research models can be used in daily life.
  5. Solve a practical problem involving resource allocation using operations research models.

CLASSWORK (5 questions):

  1. Solve the following linear programming problem: Maximize Z = 3x + 2y subject to the constraints x + 2y ≤ 8, x ≥ 0, y ≥ 0.
  2. Solve a transportation problem with the following supply and demand constraints.
  3. How would you explain the solution to a non-mathematical person?
  4. In a linear programming problem, what does the feasible region represent?
  5. What are the real-world benefits of using operations research?

ASSIGNMENT (5 tasks):

  1. Solve a linear programming problem where you maximize profit subject to production constraints.
  2. Create a transportation problem for a company and solve it using the appropriate model.
  3. Find the optimal resource allocation for a factory with limited resources.
  4. Explain how operations research can help in supply chain management.

Research the use of operations research in healthcare logistics.