Further Mathematics - Senior Secondary 1 - Models I

Models I

Get it on Google Play
Get it on the Apple App Store
  1. Home
  2. Comprehensive Lesson Plan and Notes
  3. Senior Secondary 1
  4. Models I

TERM: 3RD TERM

WEEK 6

Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Models I
Focus: Operations Research Models, Linear Programming Models, Transportation Models, Assignment Models
SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Define and distinguish different types of models in operations research.
  2. Explain the concepts and applications of linear programming models.
  3. Solve transportation problems using appropriate models.
  4. Solve assignment problems using appropriate models.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Case studies

 

INSTRUCTIONAL MATERIALS:

  • Charts illustrating different models in operations research
  • Worksheets for model application
  • Whiteboard and markers
  • Real-life examples related to operations research problems

PERIOD 1 & 2: Introduction to Operations Research Models

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of operations research and its applications. Explains that operations research uses mathematical models to solve real-life problems.

Students listen and ask clarifying questions.

Step 2 - Overview of Models

Introduces the different types of models in operations research, such as linear programming, transportation, and assignment models.

Students take notes and participate in discussion.

Step 3 - Examples

Provides examples of real-life applications for each model: Linear programming for optimizing production, transportation models for logistics, and assignment models for task allocation.

Students observe the examples and discuss their applications.

Step 4 - Distinguishing Models

Guides students in distinguishing between different models through class discussion and case studies.

Students participate in discussions and identify differences between models.

NOTE ON BOARD:

  1. Linear Programming Model: A mathematical model that optimizes a linear objective function subject to linear constraints.
  2. Transportation Model: A type of optimization model used to find the most cost-effective way to transport goods from several suppliers to several consumers.
  3. Assignment Model: A special case of the transportation model where the goal is to assign tasks to workers in a way that minimizes cost or maximizes efficiency.

EVALUATION (5 exercises):

  1. Define operations research.
  2. Name two applications of linear programming models.
  3. What is the goal of a transportation model?
  4. Explain the assignment model with an example.
  5. Distinguish between transportation and assignment models.

CLASSWORK (5 questions):

  1. Identify the model that would be used to minimize the cost of transporting goods between factories and stores.
  2. Which model would be suitable for optimizing a company's production to meet demand while minimizing costs?
  3. What is a constraint in a linear programming model?
  4. How can the assignment model be applied in a workplace setting?
  5. Explain the significance of the objective function in a linear programming model.

ASSIGNMENT (5 tasks):

  1. Research the application of operations research models in the transportation industry.
  2. Create a small-scale example of a transportation model with three suppliers and three consumers.
  3. Solve a basic linear programming problem using graphical methods.
  4. Investigate real-life applications of the assignment model in companies.
  5. Write a short report on how linear programming can be used in business decision-making.

 

PERIOD 3 & 4: Solving Linear Programming, Transportation, and Assignment Models

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Reviews the key concepts from Periods 1 & 2. Introduces the problem-solving process for linear programming, transportation, and assignment models.

Students review their notes and ask for clarification.

Step 2 - Solving Linear Programming

Demonstrates how to formulate and solve a linear programming problem using graphical methods (for two-variable problems) and Simplex method for larger problems.

Students observe and take notes.

Step 3 - Solving Transportation Models

Shows how to set up and solve transportation problems using methods such as the North-West Corner Method, Least Cost Method, and Vogel’s Approximation Method.

Students follow along and practice solving transportation problems.

Step 4 - Solving Assignment Models

Demonstrates how to solve assignment problems using the Hungarian method. Provides examples involving task allocation.

Students practice solving assignment problems in pairs.

NOTE ON BOARD:

  1. Linear Programming: Solve using graphical methods or Simplex method for higher dimensions.
  2. Transportation Models: Use methods like North-West Corner or Vogel’s Approximation to find optimal transportation routes.
  3. Assignment Models: Use the Hungarian method for task allocation problems.

EVALUATION (5 exercises):

  1. Solve the following linear programming problem graphically:
    Maximize Z = 3x + 2y, subject to constraints: x + y ≤ 4, x ≥ 0, y ≥ 0.
  2. Solve the transportation problem using the Least Cost Method:

Supply

Factory 1

Factory 2

Factory 3

Demand

A

3

2

8

15

B

6

5

4

10

C

7

4

3

20

Demand

15

10

20

  
  1. Solve the following assignment problem using the Hungarian method.
  2. Explain how to formulate a linear programming problem.
  3. Solve a small-scale transportation problem using the North-West Corner method.

CLASSWORK (5 questions):

  1. Solve the following transportation problem using Vogel’s Approximation Method.
  2. Use the Hungarian method to solve a simple assignment problem with four workers and four tasks.
  3. What is the objective function in linear programming?
  4. How do you calculate the cost in a transportation model?
  5. Describe a real-life situation where linear programming can be applied.

ASSIGNMENT (5 tasks):

  1. Solve a transportation problem involving five suppliers and four consumers.
  2. Create a linear programming problem based on a real-life scenario and solve it using graphical methods.
  3. Write an assignment problem involving task allocation for five workers.
  4. Research an organization that uses operations research models and describe how they are applied.

Solve an assignment problem using the Hungarian method and explain your solution.