IGCSE Linear Programming: Complete Guide for Cambridge IGCSE Mathematics

IGCSE linear programming is an optimization topic in Cambridge IGCSE Mathematics that appears in Paper 4 (Extended). Mastering constraints, feasible region, and optimization is essential for solving real-world optimization problems.

This comprehensive IGCSE linear programming guide covers everything you need to know, including setting up constraints, drawing feasible regions, finding optimal solutions, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to set up linear programming problems, draw feasible regions, find optimal solutions, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Linear Programming Matters

IGCSE linear programming is an essential optimization topic. Here’s why it’s so important:

• High frequency topic: Linear programming questions appear regularly in IGCSE Extended papers
• Foundation skill: Essential for optimization and decision-making problems
• Exam weight: Typically worth 8-12 marks per paper
• Real-world applications: Used in business, economics, and resource allocation
• Problem-solving skills: Develops systematic problem-solving approach

Key insight from examiners: Students often struggle with identifying constraints or finding optimal vertices. This guide will help you master these systematically.

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Understanding Linear Programming

Linear programming finds the maximum or minimum value of an objective function subject to constraints.

Steps:

1. Identify variables
2. Write constraints as inequalities
3. Draw feasible region
4. Find vertices of feasible region
5. Evaluate objective function at vertices
6. Identify optimal solution

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Setting Up Constraints

Example 1: A company makes two products. Product A needs 2 hours, Product B needs 3 hours. Total time available is 24 hours. Write the constraint.

Solution: Let x = number of Product A, y = number of Product B Constraint: 2x + 3y ≤ 24

Answer: 2x + 3y ≤ 24

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Drawing Feasible Region

Feasible region is the area satisfying all constraints.

Steps:

1. Draw each constraint line
2. Shade the correct side
3. Identify the overlapping region

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Finding Optimal Solution

Evaluate the objective function at each vertex of the feasible region.

Example 2: Maximize P = 3x + 4y subject to:

• x + y ≤ 10
• x ≥ 0, y ≥ 0

Solution: Feasible region vertices: (0, 0), (10, 0), (0, 10) Evaluate: P(0,0) = 0, P(10,0) = 30, P(0,10) = 40 Maximum: 40 at (0, 10)

Answer: Maximum P = 40 at (0, 10)

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Common Examiner Traps

• Constraint errors - Read problem carefully to identify all constraints
• Feasible region errors - Check shading is correct for each inequality
• Vertex errors - Find all vertices of the feasible region
• Objective function errors - Evaluate at all vertices

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Practice Questions

Question 1

Maximize P = 2x + 3y subject to x + y ≤ 8, x ≥ 0, y ≥ 0

Solution: Vertices: (0, 0), (8, 0), (0, 8) Evaluate: P(0,0) = 0, P(8,0) = 16, P(0,8) = 24 Maximum: 24 at (0, 8)

Answer: Maximum P = 24 at (0, 8)

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Frequently Asked Questions About IGCSE Linear Programming

What is linear programming?

Linear programming finds the maximum or minimum value of an objective function subject to linear constraints.

What is a feasible region?

The feasible region is the area on a graph that satisfies all constraints simultaneously.

How do I find the optimal solution?

Evaluate the objective function at each vertex of the feasible region. The maximum/minimum occurs at a vertex.

What are constraints?

Constraints are limitations or restrictions expressed as linear inequalities.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Linear Inequalities: Complete Guide - Master inequalities
• IGCSE Equation of a Line: Complete Guide - Master line equations
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Linear Programming with Tutopiya

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• Personalized 1-on-1 tutoring tailored to your learning pace
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Book a free IGCSE maths trial lesson and get personalized support to master linear programming and achieve your target grade.

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