Topics
Mathematical Logic
- Statements and Truth Values in Mathematical Logic
- Logical Connectives
- Tautology, Contradiction, and Contingency
- Quantifier, Quantified and Duality Statements in Logic
- Negations of Compound Statements
- Converse, Inverse, and Contrapositive
- Algebra of Statements
- Application of Logic to Switching Circuits
- Overview of Mathematical Logic
Matrices
Trigonometric Functions
Pair of Straight Lines
Vectors
Line and Plane
Linear Programming
Differentiation
- Introduction & Derivatives of Some Standard Functions
- Derivatives of Composite Functions
- Geometrical Meaning of Derivative
- Derivative of Inverse Function
- Logarithmic Differentiation
- Derivative of Implicit Functions
- Derivatives of Functions in Parametric Forms
- Higher Order Derivatives
- Overview of Differentiation
Applications of Derivatives
- Applications of Derivatives in Geometry
- Derivatives as a Rate Measure
- Approximations
- Rolle's Theorem
- Lagrange's Mean Value Theorem (LMVT)
- Increasing and Decreasing Functions
- Maxima and Minima
- Overview of Applications of Derivatives
Indefinite Integration
Definite Integration
- Definite Integral as Limit of Sum
- Integral Calculus
- Methods of Evaluation and Properties of Definite Integral
- Overview of Definite Integration
Application of Definite Integration
- Application of Definite Integration
- Area Bounded by Two Curves
- Overview of Application of Definite Integration
Differential Equations
- Basic Concepts of Differential Equations
- Order and Degree of a Differential Equation
- Formation of Differential Equations
- Methods of Solving Differential Equations> Homogeneous Differential Equations
- Methods of Solving Differential Equations>Linear Differential Equations
- Applications of Differential Equation
- Solution of a Differential Equation
- Overview of Differential Equations
Probability Distributions
- Random Variables
- Probability Distribution of Discrete Random Variables
- Probability Distribution of a Continuous Random Variable
- Variance of a Random Variable
- Expected Value and Variance of a Random Variable
- Overview of Probability Distributions
Binomial Distribution
Maharashtra State Board: Class 12
Defintion: Linear Programming Problem (L.P.P.)
A Linear Programming Problem (LPP) is a problem in which a linear objective function is to be maximised or minimised subject to a set of linear constraints and non-negative conditions on the variables.
Definition: Optimisation Problem
An optimisation problem is a problem in which the value of one quantity has to be made as large as possible or as small as possible under given restrictions. If the quantity and restrictions are linear, the problem becomes a Linear Programming Problem (LPP).
Standard Structure of an LPP
A Linear Programming Problem usually contains the following parts:
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Let the unknown quantities be represented by variables such as x and y.
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Form a linear objective function such as Z = ax + by.
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Write all restrictions as linear inequalities or equations.
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Add non-negativity restrictions: x ≥ 0, y ≥ 0.
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Solve graphically when only two variables are involved.
Real Life Examples
Example 1: Furniture Dealer
A furniture dealer deals in two items: tables and chairs. He has Rs 50,000 to invest and space for at most 60 pieces. A table costs Rs 2500 and gives a profit of Rs 250, while a chair costs Rs 500 and gives a profit of Rs 75. The problem is to decide how many tables and chairs he should buy so that total profit is maximum.
