Class 12 Maths - ISC
Linear Programming
The Linear Programming chapter in Class 12 ISC Mathematics deals with optimizing a linear objective function subject to a set of linear inequality constraints. Students learn to model real-world decision-making problems—such as allocation of resources, diet planning, and manufacturing optimization—using mathematical formulations. The chapter focuses heavily on graphical methods to solve two-variable linear programming problems, helping students identify feasible regions and determine optimal values at corner points. For ISC board exams, this is a high-scoring and mandatory topic that consistently features structured long-answer questions, making absolute graphical accuracy essential.
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 on the decision variables, usually including non-negativity restrictions like x >= 0 and y >= 0.
Feasible Region
The common region determined by all the given constraints, including the non-negativity restrictions, representing all viable solutions.
Optimal Solution
A point in the feasible region that yields the maximum or minimum value of the objective function.
Corner Point Method
A theorem stating that the optimal value of an objective function always occurs at the corner points (vertices) of the bounded feasible region.
Important Formulas
Board Exam Info
In the ISC Class 12 Mathematics exam, Linear Programming typically carries around 4 to 6 marks. Questions usually appear as a compulsory long-answer question where you must formulate the LPP from a word problem, draw an accurate graph, identify the feasible region, test corner points, and state the final optimal solution.
Frequently Asked Questions
How do I know whether to shade towards or away from the origin when graphing inequalities?
Test the origin (0,0) in the inequality. If the inequality becomes true, shade the region containing the origin; if false, shade away from it.
What is the difference between a bounded and an unbounded feasible region?
A bounded region is enclosed on all sides and has definite corner points. An unbounded region extends infinitely in one or more directions, requiring a special half-plane test to check for optimal solutions.
Why are non-negativity constraints (x >= 0, y >= 0) important in word problems?
In practical real-world scenarios, quantities of items produced, time spent, or resources used cannot be negative, so they must be restricted to the first quadrant.
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