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FMT309Sciences3 Unitsintermediate

Linear Programme 1

This course introduces students to the fundamental concepts and techniques of mathematical programming. It covers linear programming models, including formulation, the simplex method, and duality. Students will learn to solve optimization problems using graphical and algebraic methods, sensitivity analysis, and integer programming. The course also explores transportation problems and two-person zero-sum games, providing a comprehensive understanding of mathematical programming applications in various fields.

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150h
Study Time
13
Weeks
12h
Per Week
intermediate
Math Level
Course Keywords
Linear ProgrammingSimplex MethodDualityInteger ProgrammingTransportation Problem

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
📊
Math Level
Moderate Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Linear Programming Models

2

Simplex Method

3

Duality in Linear Programming

4

Integer Programming

5

Transportation Problem

6

Sensitivity Analysis

7

Artificial Variables Technique

Total Topics7 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

Assessment Methods

How your progress will be evaluated (3 methods)

Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Tutor-Marked Assessments

Comprehensive evaluation of course material understanding

Written Assessment

Final Examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Operations Research Analyst

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Management Scientist

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Logistics Coordinator

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Supply Chain Analyst

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Financial Analyst

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Industry Applications

Real-world sectors where you can apply your knowledge

ManufacturingLogisticsFinanceSupply Chain ManagementTransportation

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module I: INTRODUCTION AND FORMULATION OF LPP

4h

Unit 1: Linear Programming

4 study hours
  • •Read the course guide to understand the course structure and objectives.
  • •Study the introduction to Linear Programming in Unit 1.
  • •Familiarize yourself with the terminologies used in Linear Programming.
  • •Practice formulating LP problems from real-world scenarios.
Week
2

Module I: INTRODUCTION AND FORMULATION OF LPP

6h

Unit 1: Linear Programming

6 study hours
  • •Study the formulation of LP problems, including decision variables, objective functions, and constraints.
  • •Practice formulating LP problems from real-world scenarios.
  • •Review examples of LP problem formulations, such as the manufacturer model and the company product model.
  • •Solve Exercise 1.6.2 problems 1-4.
Week
3

Module I: INTRODUCTION AND FORMULATION OF LPP

6h

Unit 1: Linear Programming

6 study hours
  • •Study sensitivity analysis and shadow prices.
  • •Understand the economic interpretation of shadow prices.
  • •Solve Exercise 1.6.2 problems 5-8.
  • •Complete Tutor Marked Assignments (TMAs) for Module I.
Week
4

Module II: Methods of Solutions to Linear Programming Problems

5h

Unit 2: Graphical and Algebraic Methods

5 study hours
  • •Study the graphical method for solving LPPs with two decision variables.
  • •Practice solving LPPs using the graphical method.
  • •Understand the procedure for solving LPPs by the graphical method, including plotting constraints and identifying the feasible region.
  • •Solve Example 2.3.1 and 2.3.2.
Week
5

Module II: Methods of Solutions to Linear Programming Problems

5h

Unit 2: Graphical and Algebraic Methods

5 study hours
  • •Study the algebraic method for solving LPPs.
  • •Understand the relationship between the graphical and algebraic methods.
  • •Solve Exercise 2.6.1 problems 1-5.
  • •Complete Tutor Marked Assignments (TMAs) for Module II.
Week
6

Module II: Methods of Solutions to Linear Programming Problems

6h

Unit 3: Simplex Algorithm (Algebraic and Tabular Forms)

6 study hours
  • •Study the algebraic simplex method for solving LPPs.
  • •Understand the steps involved in the algebraic simplex method.
  • •Solve Example 3.3.1 using the algebraic simplex method.
  • •Solve Exercise 3.6.1 problems 1-4.
Week
7

Module II: Methods of Solutions to Linear Programming Problems

6h

Unit 3: Simplex Algorithm (Algebraic and Tabular Forms)

6 study hours
  • •Study the tabular form of the simplex method.
  • •Understand the concept of pivoting and how to find an improved solution.
  • •Solve Example 3.3.2 using the tabular form of the simplex method.
  • •Solve Exercise 3.6.1 problems 5-8.
Week
8

Module II: Methods of Solutions to Linear Programming Problems

6h

Unit 3: Simplex Algorithm (Algebraic and Tabular Forms)

6 study hours
  • •Study the applications of the simplex method, including maximum profit and media selection problems.
  • •Solve Example 3.3.5 and 3.3.6.
  • •Solve Exercise 3.6.1 problems 9-12.
  • •Complete Tutor Marked Assignments (TMAs) for Module II.
Week
9

Module II: Methods of Solutions to Linear Programming Problems

6h

Unit 4: Artificial Variables Technique

6 study hours
  • •Study the Charne's Big M method for solving LPPs with artificial variables.
  • •Understand the steps involved in the Big M method.
  • •Solve Example 4.3.1 using the Big M method.
  • •Solve Exercise 4.6.1 problems 1-3.
Week
10

Module II: Methods of Solutions to Linear Programming Problems

6h

Unit 4: Artificial Variables Technique

6 study hours
  • •Study the two-phase simplex method for solving LPPs with artificial variables.
  • •Understand the steps involved in the two-phase simplex method.
  • •Solve Example 4.3.4 using the two-phase simplex method.
  • •Solve Exercise 4.6.1 problems 4-6.
Week
11

Module II: Methods of Solutions to Linear Programming Problems

6h

Unit 5: Simplex Algorithm- Initialization and Iteration

6 study hours
  • •Study initialization and iteration in the simplex algorithm.
  • •Understand how to handle degeneracy in LPPs.
  • •Study methods to resolve degeneracy, such as rearranging columns and finding minimum ratios.
  • •Solve Example 5.3.3 and 5.3.4.
Week
12

Module II: Methods of Solutions to Linear Programming Problems

6h

Unit 5: Simplex Algorithm- Initialization and Iteration

6 study hours
  • •Study termination conditions in the simplex algorithm, including alternate optimum, unboundedness, infeasibility, and cycling.
  • •Understand how to identify and handle alternate optimum solutions.
  • •Solve Example 5.3.5 and 5.3.6.
  • •Solve Exercise 5.6.1 problems 1-4.
Week
13

Module III: DUALITY IN LINEAR PROGRAMMING

12h

Unit 6: Duality in Linear Programming

6 study hours
  • •Study duality in linear programming, including formulation of dual problems and important results in duality.
  • •Understand the definition of a dual problem and how to formulate it.
  • •Solve Example 6.3.1 and 6.3.2.
  • •Solve Exercise 6.6.1 problems 1-4.

Unit 7: Transportation Problem

6 study hours
  • •Study the dual simplex method and sensitivity analysis.
  • •Understand the dual simplex algorithm and how to perform sensitivity analysis.
  • •Solve Example 6.3.7 and 6.3.8.
  • •Complete Tutor Marked Assignments (TMAs) for Module III.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Thoroughly review all worked examples in the study units, focusing on the step-by-step application of each method.

2

Practice formulating linear programming models from diverse scenarios, paying close attention to defining decision variables, objective functions, and constraints.

3

Create concept maps linking the simplex method, duality, and sensitivity analysis to understand their interrelationships.

4

Focus on mastering the simplex method, including initialization, iteration, and termination conditions.

5

Practice solving transportation problems using different methods (NWCR, Least Cost, VAM) and optimizing with the MODI method.

6

Review the assumptions and limitations of linear programming and integer programming.

7

Pay special attention to the economic interpretation of dual variables and shadow prices.

8

Work through all Tutor-Marked Assignments (TMAs) and self-assessment exercises to reinforce understanding and identify areas for improvement.

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