Class 12 Mathematics — Chapter 6: LINEAR PROGRAMMING

What you'll learn

• ▸Introduction to Linear Programming Problems (LPP)
• ▸Mathematical Formulation of LPP
• ▸Objective Function and Constraints
• ▸Graphical Method: Feasible Region
• ▸Feasible and Infeasible Solutions
• ▸Optimal Solution and the Corner Point Method
• ▸Bounded and Unbounded Feasible Regions

Chapter Summary

--- PAGE 1 --- 12080CH12 Chapter 12 LINEAR PROGRAMMING ❖ *The mathematical experience of the student is incomplete if he never had the opportunity to solve a problem invented by himself. – G. POLYA* ❖ 12.1 Introduction In earlier classes, we have discussed systems of linear equations and their applications in day to day problems. In Class XI, we have studied linear inequalities and systems of linear inequalities in two variables and their solutions by graphical method. Many applications in mathematics involve systems of inequalities/equations. In this chapter, we shall apply the systems of linear inequalities/equations to solve some real life problems of the type as given below: A furniture dealer deals in only two items – tables and chairs. He has Rs 50,000 to invest and has storage space of at most 60 pieces. A table costs Rs 2500 and a chair Rs 500. He estimates that from the sale of one table, he can make a profit of Rs 250 and that from the sale of one chair a profit of Rs 75. …

Practice Questions from this Chapter

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1. Show real-world optimization problems. Get Solution →
2. Explain linear programming simply. Get Solution →
3. List daily examples of constraints. Get Solution →
4. What is the general class of problems that seek to maximise profit or minimise cost called? Get Solution →
5. What is the linear function Z = ax + by, which has to be maximised or minimized, called? Get Solution →
6. In a linear programming problem, what are the linear inequalities or restrictions on the variables called? Get Solution →
7. The conditions x ≥ 0, y ≥ 0 in a linear programming problem are known as what? Get Solution →
8. What is the common region determined by all the constraints, including non-negative constraints, of a linear programming problem called? Get Solution →

Did you know?

• 💡 Bees build hexagonal honeycomb cells for optimal storage of honey and pollen.
• 💡 Linear programming was secretly developed during World War II for military logistics.
• 💡 Your brain constantly optimizes decisions, even when choosing the fastest checkout line.
• 💡 Ancient Egyptians optimized pyramid construction by using basic geometry and resource planning.
• 💡 Traffic lights use optimization algorithms to minimize wait times and improve city flow.

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