Business Mathematics : For University of Delhi

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Cover Contents Syllabus Preface Chapter 1: Matrices and Determinants Introduction Equality of Matrices Types of Matrices Algebra of Matrices Addition of Matrices Properties of Matrix Additioin Scalar Multiplication Properties of Scalar Multiplication Multiplication of Matrices Properties of Matrix Multiplication Positive Integral Powers of a Square Matrix Matrix Polynomial Exercises Answers Hints to Selected Problems Transpose of a Matrix Properties of the Transpose of a Matrix Symmetric Matrix Trick(s) for Problem Solving Skew Symmetric Matrix Trick(s) for Problem Solving Exercises Answers Determinants Determinant of a Square Matrix of Order 1 Determinant of a Square Matrix of Order 2 Determinant of a Square Matrix of Order 3 Sarrus Diagram for Expansion of a Determinant of Order 3 Properties of Determinants Exercises Answers Hints to Selected Problems Cramer’s Rule for Solving a System of Linear Equations Exercises Answers Minors and Cofactors Adjoint of a Matrix Singular and Non-singular Matrices Inverse of a Matrix Important Properties of the Inverse of a Matrix Formula for Finding A–1 Exercises Answers Hints to Selected Problems Solving a System of Linear Equations by Matrix Method Elementary Row Transformations Gauss-Jordan Method for Finding Inverse of a Matrix Solution of Linear Equations by Gauss-Jordan Method Exercises Answers Chapter 2: Applications of Matrices Introduction Exercises Answers Hints to Selected Problems Systems of Linear Equations Exercises Answers Hints to Selected Problems Input-Output Analysis (Leontief’s Models) Hawkins–Simon Conditions for the Viability of the System Technology Matrix in Value Terms Closed and Open Input-Output Models Closed Input-Output Model Open Input-output Model Determination of Equilibrium Prices Exercises Answers Hints to Selected Problems Chapter 3: Linear Programming General Form of a Linear Programming Problem Formulation of the Problem Exercises Answers Hints to Selected Problems Solution of a Linear Programming Problem Some Basic Definitions Solution by Graphical Method Extreme Point Theorem Special Cases in Linear Programming Exercises Answers Hints to Selected Problems Simplex Method Some Basic Definitions Computational Procedure in Simplex Method Step 1. Formulation of the Problem into a Linear Programming Model Step 2. Converting Inequalities into Equations Step 3. Finding the Initial Basic Feasible Solution Step 4. Developing the Initial Simplex Table Step 5. Performing the Optimality Test Step 6. Selecting the Entering and Departing Variable Step 6. Selecting the Entering and Departing Variable Step 7. Developing the Second simplex Table Step 8. Check for the Optimality Exceptional Cases Encountered During Simplex Method Multiple Optimal solution Artificial Variable Technique (The Big M-Method) Concept of Duality Dual of General Linear Programming Problem Relationship Between Primal and its Dual Advantages of Duality Economic Interpretation of the Dual Caution Economic Interpretation Two Phase Method Exercises Answers Hints to Selected Problems Chapter 4: Limits and Continuity Limit of a Function Algebra of limits Evaluation of Limits Type I. Direct Substitution Type II. Factorization Type III. Rationalization Infinite Limits Some Important Limits Economic Interpretation Exercises Answers Hints to Selected Problems Continuity Continuity on an Interval Continuous Functions Properties of Continuous Functions Exercises Answers Hints to Selected Problems Chapter 5: Differentiation Derivative of a Function Geometrical Interpretation of the Derivative Some Formulae Derivative of Implicit Functions Logarithmic Differentiation Differentiation of Parametric Forms Exercises Answers Hints to Selected Problems Applications of Derivatives Increasing and Decreasing Functions Maxima and Minima Concavity and Convexity Exercises Answers Hints to Selected Problems Chapter 6: Applications of Derivatives in Economics Demand Function Supply Function Cost Function Revenue Function Profit Function Market Equilibrium Tax (Subsidy) and Market Equilibrium Average Cost Marginal Cost Relationship between Average Cost and Marginal Cost Average Revenue and Marginal Revenue Propensities to Consume and Save The Marginal Propensity to Save (MPS) Exercises Answers Hints to Selected Problems The Concept of Elasticity Elasticity of Demand Kinds of Elasticity of Demand Relationship between Marginal Revenue, Average Revenue and Elasticity of Demand Elasticity of Supply Income Elasticity of Demand Cost Elasticity Exercises Answers Hints to selected Problems Applications of Maxima and Minima Maximization of Total Revenue Exercises Answers Hints to Selected Problems Minimization of Cost Exercises Answers Hints to Selected Problems Maximization of Profit Profit Maximization Under Monopoly Profit Maximization Under Perfect Competition Exercises Answers Hints to Selected Problems Effect of Taxes and Subsidies on Profit Imposition of Sales Tax Offer of Subsidy Maximization of Tax Revenue Exercises Answers Inventory Control Exercises Answers Hints to Selected Problems Chapter 7: Partial Differentiation Introduction Partial Derivatives Second Order Partial Derivatives Total Differential Second Order Total Differentials Differentiation of Implicit Functions Exercises Answers Hints to Selected Problems Homogeneous Functions Exercises Answer Hints to Selected Problems Maxima and Minima of Functions of Two Variables Exercises Answer Hints to Selected Problems Chapter 8: Economic Applications of Partial Derivatives Demand Analysis Nature of Commodities Partial Elasticities Exercises Answers Hints to Selected Problems Optimization Problems Monopoly and joint Production Discriminating Monopoly Price Discrimination and Price Elasticity of Demand Duopoly Exercises Answers The Utility Function Price Line or Budget Line (or Budget Constraint) Utility Maximization (Constrained Maximization) Exercises Answers Hints to Selected Problems Production Function Marginal Productivity Average Productivity Degree of an Homogeneous Production Function The Linear Homogeneous Production Function Cobb-Douglas Production Function Isoquants Elasticity of Substitution Exercises Answers Hints to Selected Problems Marginal Rate of Technical Substitution (MRTS) Exercises Answers Hints to Selected Problems Chapter 9: Integration Introduction Exercises Answer Hints to Selected Problems Methods of Integration Exercises Answers Hints to Selected Problems Integration by Parts Exercises Answers Hints to Selected Problems Integration of Rational Functions Exercises Answers Hints to Selected Problems Definite Integral Definite Integral as Area Under a Curve Exercises Answers Hints to Selected Problems Chapter 10: Applications of Integration Introduction From a Marginal Cost Function to Its Total Cost Function Exercises Answers Hints to Selected Problems From a Marginal Revenue Function to Its Total Revenue Function and the Demand Function Exercises Answers Hints to Selected Problems From Marginal Propensity to Consume to Its Consumption Function Exercises Answers From Price Elasticity of Demand to the Demand Function Exercises Answers Hints to Selected Problems Maximum Profits When Marginal Revenue and Marginal Cost Functions are Given Exercises Answers Consumer and Producer Surplus Consumer Surplus Under Pure Competition Consumer Surplus Under Monopoly Exercises Answers Hints to Selected Problems Rate of Growth or Sale Exercises Answers Hints to Selected Problems Capital Formation Exercises Answers Hints to Selected Problems Learning Curve Exercises Answers Hints to Selected Problems Chapter 11: Mathematics of Finance Introduction Interest Simple Interest Exercises Answers Hints to Selected Problems Compound Interest Continuous Compounding Exercises Answers Hints to Selected Problems Nominal and Effective Rate of Interest Relation Between the Effective Rate of Interest and the Nominal Rate of Interest Exercises Answers Present Value or Capital Value Exercises Answers Hints to Selected Problems Equation of Value Exercises Answers Hints to Selected Problems Discount Nominal and Effective Rates of Discount Exercises Answers Depreciation Exercises Answers Hints to Selected Problems Annuity Periodic Payment Payment Period Term Types of Annuities Exercises Answers Hints to Selected Problems Sinking Fund Exercises Answers Hints to Selected Problems Present Value of an Ordinary Annuity Exercises Answers Hints to Selected Problems Annuity Due Amount of an Annuity Due Present Value of an Annuity Due Exercises Answers Deferred Annuity Amount of a Deferred Annuity Exercises Answers Hints to Selected Problems Amortization Perpetuity Present Value of a Deferred Perpetuity Exercises Answers Chapter 12: Assignment Problem Introduction The Assignment Model Mathematical Representation of Assignment Model Solution method of Assignment Problem Step I: Find the Opportunity Cost Table by Step II: Make Assignment in the Matrix Obtained in Step 1 in the Following Way: Step III: Step4: Develop the new Revised Opportunity Cost Table: Unbalanced Assignment Problem Chapter 13: Transportation Problem Introduction General Transportation Problem The Transportation Tableau Solution of a Transportation Problem Loops in Transportation Table Methods for Finding Initial Solutions Least Cost Method (LCM) Vogel’s Approximation Method (VAM) Test for Optimality Stepping Stone Method Unbalanced Transportation Problem Maximization Transportation Problem Exercises Answers Tables Previous Years’ University Questions with Solutions