Class 12 Maths - WEST-BENGAL
Linear Programming
The Linear Programming chapter in Class 12 Mathematics under the West Bengal Council of Higher Secondary Education (WBCHSE) deals with optimizing a linear objective function subject to a set of linear inequalities called constraints. This chapter is vital for board exams as it consistently features a high-weightage long-answer question (usually 5 marks) where students must graphically solve maximization or minimization problems. Mastering this topic not only guarantees scoring marks in the board exams but also builds foundational optimization skills used in economics, commerce, and industry.
Start Learning FreeKey Concepts
Objective Function
A linear function Z = ax + by whose value is to be maximized or minimized under given constraints.
Constraints
Linear inequalities or equations representing limitations on the resource 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 valid solutions.
Optimal Solution
A point in the feasible region that yields the maximum or minimum value of the objective function.
Corner Point Method
A graphical method to solve LPP by evaluating the objective function only at the corner vertices of the feasible region.
Important Formulas
Board Exam Info
In the West Bengal (WBCHSE) Class 12 Mathematics board examination, Linear Programming typically carries around 5 to 6 marks. The standard question pattern includes one compulsory long-answer question (LAQ) worth 5 marks, requiring students to formulate and graphically solve a word problem involving maximization or minimization.
Frequently Asked Questions
Is it mandatory to shade the feasible region in the WBCHSE board exam?
Yes, clearly shading the feasible region and labeling the corner points with coordinates is essential to get full marks in the graphical method.
What if the feasible region is unbounded?
If the feasible region is unbounded, the maximum or minimum value may not exist. A test (like drawing a half-plane for Z > Z0) is used to check if the optimal solution actually exists at a corner point.
Can I use the simplex method for Class 12 WBCHSE exams?
No, the WBCHSE Class 12 syllabus strictly requires the graphical method for solving Linear Programming Problems with two variables.
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