Class 12 Maths - ODISHA
Linear Programming
The chapter 'Linear Programming' in Class 12 Mathematics for Odisha (BSE) students deals with optimizing a linear objective function subject to a set of linear inequality constraints. It bridges algebra and real-world decision-making, showing how to maximize profits or minimize costs in business and industry. In board exams, this is a high-scoring chapter, typically featuring a mandatory long-answer question where you must graphically solve a linear programming problem involving corner points.
Start Learning FreeKey Concepts
Objective Function
A linear function Z = ax + by whose maximum or minimum value is to be found under given conditions.
Constraints
Linear inequalities or equations representing restrictions or limitations on the variables x and y.
Feasible Region
The common region determined by all the given constraints, including non-negative restrictions, where all inequalities are satisfied.
Optimal Solution
A point in the feasible region that gives the maximum or minimum value of the objective function.
Corner Point Method
A graphical method where the optimal value of Z always occurs at the corner points (vertices) of the bounded feasible region.
Important Formulas
Board Exam Info
In the Odisha (BSE) Class 12 Mathematics board examination, Linear Programming typically carries around 6 to 8 marks. The questions mostly consist of one long-answer (LA) question requiring the graphical solution of a word problem involving maximization or minimization.
Frequently Asked Questions
How do I know whether to shade towards the origin or away from it?
Test the origin (0,0) in the inequality. If the statement is true, shade towards the origin; if false, shade away from it.
What is the difference between bounded and unbounded feasible regions?
A bounded region is enclosed completely with finite boundaries where the maximum and minimum always exist. An unbounded region extends infinitely, requiring a special test to check if an optimal solution actually exists.
Do I need to draw the graph on graph paper for the board exam?
Yes, for BSE Odisha board exams, solving graphical Linear Programming problems accurately requires plotting the constraints on a graph paper attached to your answer booklet.
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