Class 12 Maths - MAHARASHTRA
Linear Programming
The Linear Programming chapter in Class 12 Mathematics (Maharashtra State Board) deals with optimizing a linear objective function subject to a set of linear inequality constraints. It bridges algebraic modeling with graphical visualization to solve real-world decision-making problems, such as maximizing profit or minimizing cost. For the Maharashtra board exams, this is a high-scoring chapter that consistently features standard graphical questions in Section D, making mastery of region shading and corner point evaluation essential for securing top marks.
Start Learning FreeKey Concepts
Linear Programming Problem (LPP)
A mathematical technique used to find the best possible outcome in a mathematical model whose requirements are represented by linear relationships.
Objective Function
A linear function Z = ax + by that needs to be maximized or minimized based on the given constraints.
Constraints
Linear inequalities or equations representing the limitations or restrictions on the resources in a given problem.
Feasible Region
The common region determined by all the given constraints, including non-negative constraints, which satisfies all conditions.
Corner Point Method
A method to find the optimal solution by evaluating the objective function at the vertices (corner points) of the feasible region.
Important Formulas
Board Exam Info
In the Maharashtra (MSBSHSE) Class 12 Mathematics board examination, Linear Programming typically carries around 4 to 6 marks. Questions usually appear as a full-length 4-mark or 5-mark question requiring students to draw a graph, shade the feasible region, identify corner points, and find the optimal value.
Frequently Asked Questions
How do I know which side of the line to shade?
Substitute the origin (0,0) into the inequality. If the statement is true, shade the side containing the origin; if false, shade the opposite side.
Is it mandatory to draw graphs using a graph paper in the board exam?
Yes, for LPP questions in the Maharashtra board exam, you must draw the graph neatly on the provided graph paper and attach it to your answer booklet.
What are non-negative constraints and why are they important?
Constraints like x >= 0 and y >= 0 ensure that the solution lies in the first quadrant, which is standard for practical problems where quantities cannot be negative.
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