Linear Programme 1
- Sciences
- 300 level
- 3 credit units
- 219 pages
- 8 units
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.
About this course
- Difficulty
- Intermediate
- Study hours
- 150 hours
- Maths
- Intermediate
- Content
- Theoretical, practical, problem solving
- Practical work
- No
- Assignments
- Tutor Marked Assessments
- Final Examination
What you'll read
The real module and unit structure of FMT309, taken from the course material NOUN publishes.
- UNIT 1: LINEAR PROGRAMMINGPage 6
- UNIT 2 GRAPHICAL AND ALGEBRAIC METHODS.Page 25
- UNIT 3 SIMPLEX ALGORITHM (ALGEBRAIC AND TABULAR FORMS)Page 45
- UNIT 4: ARTIFICIAL VARIABLES TECHNIQUEPage 83
- UNIT 5: SIMPLEX ALGORITHM- INITIALIZATION AND ITERATIONPage 97
- UNIT 6: DUALITY IN LINEAR PROGRAMMINGPage 125
- UNIT 7 TRANSPORTATION PROBLEMPage 159
- UNIT 8: INTEGER PROGRAMMINGPage 182
One paragraph, so you can see how it reads
FMT309 · UNIT 1: LINEAR PROGRAMMING
The Simplex method which is the most popular and powerful tool for solving linear pro- gramming, to be studied in full later in this course, was published by Dantzig in 1949.
What you should be able to do
- Formulate linear programming models for various real-world problems.
- Solve linear programming problems using the simplex method.
- Apply duality theory to solve linear programming problems.
- Solve integer programming problems using cutting plane and branch and bound methods.
- Analyze transportation problems and find optimal solutions.
- Perform sensitivity analysis to assess the impact of changes in problem parameters.
What it prepares you for
- Operations Research Analyst
- Management Scientist
- Logistics Coordinator
- Supply Chain Analyst
- Financial Analyst
- Manufacturing
- Logistics
- Finance
- Supply Chain Management
- Transportation
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module II: Methods of Solutions to Linear Programming Problems
Unit 3: Simplex Algorithm (Algebraic and Tabular Forms)
The algebraic simplex method requires careful attention to detail and can be computationally intensive, especially with a large number of variables and constraints.
- Module II: Methods of Solutions to Linear Programming Problems
Unit 4: Artificial Variables Technique
Understanding and applying the Big M method requires careful handling of artificial variables and the penalty term to ensure feasibility and optimality.
- Module III: DUALITY IN LINEAR PROGRAMMING
Unit 6: Duality in Linear Programming
Formulating the dual problem and interpreting the dual variables requires a strong understanding of linear programming theory and economic principles.
A suggested way through it
13 weeks, about 80 hours in total. Yours will differ.
- Week 1Module I: INTRODUCTION AND FORMULATION OF LPP
Unit 1: Linear Programming · 4 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 2Module I: INTRODUCTION AND FORMULATION OF LPP
Unit 1: Linear Programming · 6 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 3Module I: INTRODUCTION AND FORMULATION OF LPP
Unit 1: Linear Programming · 6 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 4Module II: Methods of Solutions to Linear Programming Problems
Unit 2: Graphical and Algebraic Methods · 5 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 5Module II: Methods of Solutions to Linear Programming Problems
Unit 2: Graphical and Algebraic Methods · 5 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 6Module II: Methods of Solutions to Linear Programming Problems
Unit 3: Simplex Algorithm (Algebraic and Tabular Forms) · 6 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 7Module II: Methods of Solutions to Linear Programming Problems
Unit 3: Simplex Algorithm (Algebraic and Tabular Forms) · 6 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 8Module II: Methods of Solutions to Linear Programming Problems
Unit 3: Simplex Algorithm (Algebraic and Tabular Forms) · 6 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 9Module II: Methods of Solutions to Linear Programming Problems
Unit 4: Artificial Variables Technique · 6 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 10Module II: Methods of Solutions to Linear Programming Problems
Unit 4: Artificial Variables Technique · 6 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 11Module II: Methods of Solutions to Linear Programming Problems
Unit 5: Simplex Algorithm- Initialization and Iteration · 6 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 12Module II: Methods of Solutions to Linear Programming Problems
Unit 5: Simplex Algorithm- Initialization and Iteration · 6 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 13Module III: DUALITY IN LINEAR PROGRAMMING
Unit 6: Duality in Linear Programming · 6 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 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..
Preparing for the exam
- Thoroughly review all worked examples in the study units, focusing on the step-by-step application of each method.
- Practice formulating linear programming models from diverse scenarios, paying close attention to defining decision variables, objective functions, and constraints.
- Create concept maps linking the simplex method, duality, and sensitivity analysis to understand their interrelationships.
- Focus on mastering the simplex method, including initialization, iteration, and termination conditions.
- Practice solving transportation problems using different methods (NWCR, Least Cost, VAM) and optimizing with the MODI method.
- Review the assumptions and limitations of linear programming and integer programming.
- Pay special attention to the economic interpretation of dual variables and shadow prices.
- Work through all Tutor-Marked Assignments (TMAs) and self-assessment exercises to reinforce understanding and identify areas for improvement.
Questions students ask about this course
What is FMT309 about?
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.
How many units does FMT309 have?
FMT309, Linear Programme 1, has 8 units across 1 module, over 219 pages of course material. You can read it one unit at a time.
How many credit units is FMT309?
FMT309 carries 3 credit units, at 300 level in Sciences.
Is FMT309 hard?
FMT309 is rated intermediate level, with intermediate mathematical content. It is mostly theoretical, practical and problem solving work.
How long does FMT309 take to study?
About 150 hours of study, spread across its 8 units.
How is FMT309 assessed?
FMT309 is assessed by Assignments, Tutor Marked Assessments and Final Examination.
What can I do with FMT309?
Operations Research Analyst, Management Scientist, Logistics Coordinator, Supply Chain Analyst and Financial Analyst.