Class 12 Maths - GUJARAT
Linear Programming
The Chapter 'Linear Programming' in Class 12 Mathematics for GSEB students deals with optimizing a linear objective function subject to a set of linear inequalities called constraints. It has wide real-world applications in business, manufacturing, and resource allocation. For board exams, this is a high-scoring chapter where questions typically involve graphing inequalities, identifying the feasible region, and finding the optimal solution at corner points. Mastering this chapter ensures you secure easy marks by following a systematic, step-by-step graphical approach.
Start Learning FreeKey Concepts
Linear Programming Problem (LPP)
A problem that aims to maximize or minimize a linear function subject to certain conditions or linear constraints.
Objective Function
The linear function Z = ax + by that needs to be maximized or optimized based on the given constraints.
Constraints
The linear inequalities or equations restricting the variables, usually including non-negativity restrictions like x ≥ 0 and y ≥ 0.
Feasible Region
The common region determined by all the given constraints including non-negativity restrictions, representing all valid solutions.
Corner Point Method
A method to solve LPP by evaluating the objective function at the vertices (corner points) of the feasible region.
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 12 Mathematics board examination, Linear Programming usually carries around 4 to 6 marks. Questions typically include one long 4-mark word problem where you have to formulate the LPP and solve it graphically to find the maximum or minimum value.
Frequently Asked Questions
How do I know whether to shade towards or away from the origin for an inequality?
Substitute the origin (0,0) into the inequality. If the resulting statement is true, shade towards the origin; if false, shade away from it.
What is the difference between a bounded and an unbounded feasible region?
A bounded region is enclosed completely and has definite corner points. An unbounded region extends infinitely in one or more directions, requiring special rules to check for optimal solutions.
Are the non-negativity constraints x ≥ 0 and y ≥ 0 compulsory to write?
Yes, unless specified otherwise in the word problem, they ensure that the solution lies in the first quadrant, which is standard for practical real-world applications.
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