Class 12 Maths - MP
Linear Programming
The Chapter 'Linear Programming' in Class 12 Mathematics for MPBSE students deals with optimizing a linear objective function subject to a set of linear inequalities called constraints. It is a powerful mathematical technique used in various fields like resource allocation, manufacturing, and transportation to find the maximum or minimum possible value. For MPBSE board exams, this chapter is extremely scoring because the methodology is algorithmic and graphical. Students frequently encounter long-answer questions requiring the graphical solution of linear programming problems, making it a crucial chapter to secure high marks.
Start Learning FreeKey Concepts
Objective Function
A linear function Z = ax + by whose maximum or minimum value is to be found under given constraints.
Constraints
Linear inequalities or equations representing conditions or restrictions on the variables of a linear programming problem.
Feasible Region
The common region determined by all the given constraints including non-negative constraints (x ≥ 0, y ≥ 0), representing 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 method to solve LPP graphically by evaluating the objective function only at the corner points of the bounded feasible region.
Important Formulas
Board Exam Info
In the Madhya Pradesh (MPBSE) Class 12 Mathematics board examination, Linear Programming typically carries around 4 to 6 marks. Questions usually include one long-answer type question where students must draw a graph, shade the feasible region, find the corner points, and determine the optimal value of the objective function.
Frequently Asked Questions
What is the difference between bounded and unbounded feasible regions?
A bounded region is enclosed within a finite area on the graph where corner points can be easily tested. An unbounded region extends infinitely in one or more directions, requiring special conditions to determine the maximum or minimum.
Are non-negative constraints compulsory in every LPP?
Yes, constraints like x ≥ 0 and y ≥ 0 are almost always present in practical problems because quantities like items produced, time, or cost cannot be negative.
How many marks is the graphical LPP question worth in the MPBSE exam?
Usually, it comes as a 4-mark or 5-mark long answer question requiring step-by-step graphical representation and calculation.
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