Class 12 Maths - BIHAR
Linear Programming
The Linear Programming chapter in Class 12 Mathematics helps students optimize a linear objective function subject to a set of linear inequality constraints. This powerful mathematical technique has vast real-world applications in business, industry, and resource allocation. For Bihar Board (BSEB) students, this is a highly scoring chapter. Board exams regularly feature standard long-answer questions requiring graphical solutions to find maximum or minimum values of objective functions. Mastering this chapter guarantees you secure full marks in the graphical optimization section, making it an essential scoring opportunity.
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 limitations or restrictions on the variables x and y.
Feasible Region
The common region determined by all the given constraints including non-negative restrictions x ≥ 0, y ≥ 0.
Corner Point Method
A systematic method to solve LPP by evaluating the objective function at the vertices (corner points) of the feasible region.
Unbounded Region
A feasible region that does not extend infinitely in all directions but may have an infinite area, where maximum or minimum might not always exist.
Important Formulas
Board Exam Info
In the Bihar (BSEB) Class 12 Mathematics exam, Linear Programming typically carries around 5 to 8 marks. Questions usually include one objective/short-answer question and one compulsory 5-mark long-answer question where you must draw a graph to find the optimal solution.
Frequently Asked Questions
Is graph paper provided in the BSEB Class 12 exam for solving LPP?
Yes, graph sheets are provided during the board exam for drawing accurate constraint lines and finding the feasible region.
How do I know whether to maximize or minimize the objective function?
The question itself will explicitly state whether you need to maximize (e.g., profit) or minimize (e.g., cost).
What if the feasible region is unbounded?
If the region is unbounded, a maximum or minimum may not exist. If it does exist, it must occur at a corner point, but you must check using the half-plane test.
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