Class 12 Maths - RAJASTHAN
Linear Programming
The chapter 'Linear Programming' in Class 12 Mathematics under the Rajasthan Board (RBSE) deals with optimization problems where a linear objective function must be maximized or minimized subject to certain linear constraints. Linear programming has vast real-world applications in industry, agriculture, and economics, such as resource allocation, diet planning, and transportation. In board exams, this chapter is a scoring area, usually featuring a long-answer question where you must graphically solve a problem with multiple constraints to find the optimal solution.
Start Learning FreeKey Concepts
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 limitations or restrictions on the decision variables x and y, usually including non-negativity constraints x ≥ 0 and y ≥ 0.
Feasible Region
The common region determined by all the given constraints, including the non-negativity restrictions, representing all acceptable 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 of solving LPP by evaluating the objective function at the corner points of the feasible region to find the optimal value.
Important Formulas
Board Exam Info
In the Rajasthan (RBSE) Class 12 Mathematics board examination, Linear Programming typically carries around 4 to 6 marks. The pattern usually features one long-answer question (worth 4 or 6 marks) requiring graph plotting and step-by-step optimization.
Frequently Asked Questions
Do I need to shade the feasible region or the non-feasible region in the RBSE exam?
It is best practice to shade or highlight the feasible region clearly and label it so the examiner can easily identify it.
What should I do if the feasible region is unbounded?
If the feasible region is unbounded, maximum or minimum may not exist. Check if Z > ax + by has points in the feasible region to confirm if a maximum exists.
Are the non-negativity constraints (x ≥ 0, y ≥ 0) mandatory to mention?
Yes, unless stated otherwise in the problem, real-world variables cannot be negative, so including x ≥ 0 and y ≥ 0 is compulsory.
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