Class 12 Maths - HARYANA
Linear Programming
The chapter 'Linear Programming' in Class 12 Mathematics for Haryana (BSEH) board helps students optimize a given objective function subject to a set of linear constraints. It deals with real-world decision-making problems, such as maximizing profit or minimizing cost. You will learn to formulate linear programming problems (LPP), graph feasible regions, and find optimal solutions using corner point methods. This chapter is a high-scoring section in the board examinations, usually featuring long-answer questions that test your graphical plotting and analytical skills.
Start Learning FreeKey Concepts
Objective Function
A linear function Z = ax + by that needs to be maximized or minimized under given constraints.
Constraints
Linear inequalities or equations representing restrictions or limitations on the variables x and y.
Feasible Region
The common region determined by all the given constraints including non-negative constraints (x >= 0, y >= 0).
Corner Point Method
A method to find the optimal value of Z by evaluating the objective function at the vertices of the feasible region.
Optimal Solution
Any point in the feasible region that gives the maximum or minimum value of the objective function.
Important Formulas
Board Exam Info
In the Haryana (BSEH) Class 12 Mathematics exam, Linear Programming typically carries around 5 to 6 marks. It generally features one long-answer question (5 marks) where students are required to formulate an LPP from a word problem and solve it graphically.
Frequently Asked Questions
How do I know whether to shade towards or away from the origin for an inequality?
Test the origin (0,0) in the inequality. If the statement is true, shade the side containing the origin; if false, shade the opposite side.
Is it mandatory to include non-negative constraints like x >= 0 and y >= 0?
Yes, unless stated otherwise, quantities in practical problems cannot be negative, so non-negative constraints must always be included.
What is the difference bounded and unbounded feasible regions?
A bounded region is enclosed completely within boundaries where the maximum and minimum always exist. An unbounded region extends infinitely, and testing for optimization has special rules.
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