Vuhelper

08-12-2014, 02:02 AM

BBA-135 Business Mathematic Assignment No. 1 & 2 Spring Semester 201

ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD

(Department of Business Administration)

BUSINESS MATHEMATICS (BBA-135)

(CHECKLIST)

SEMESTER: SPRING 2014

This packet comprises the following material:

1. Text Book (one)

2. Course Outline

3. Assignment No. 1 & 2

4. Assignment Forms (2 sets)

If you find anything missing out of the above-mentioned material, please contact at the address given below:

Mailing Officer

Mailing Section, Block No. 28

Allama Iqbal Open University

H-8, ISLAMABAD

Phone: 051-9057611-12

Course Coordinator

ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD

(Department of Business Administration)

WARNING

1. PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.

2. SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM OTHER(S) AS ONES OWN WILL BE PENALIZED AS DEFINED IN AIOU PLAGIARISM POLICY.

ASSIGNMENT No. 1

(Units: 15)

Course: Business Mathematics (135) Semester: Spring 2014

Level: BBA Total Marks: 100

Pass Marks: 40

Note: All questions are compulsory and carry equal marks.

Q. 1 (a) Let A={2,4,6,8,10], B={6,8,11,12} and U={1,2,3,4,5,6,7,8,9,10,11,12}

Find

(1) Ac (2) AB (3) (AB)c (4) AB

(b) A store manager plans to increase the selling price of an item by 7%. If the item costs $6.52 and presently sells for $8.95. How much increase in price occurs after the increase in selling price.

(c) Find the equation of a line containing the points (4, 7) and 3, 6). (20)

Q. 2 (a) A service industry Williamss system has the following input coefficient matrix.

Services

Manufacturing

Farming

If the demand from the consumer section are 21, 5 and 1 units respectively. Find the output needed for these demands.

(b) Find the solution set of the following equations:

1. 6x + 2y = 6 and 12x + 4y = 12

2. 0.02x 0.4y = 0.2; and 0.04x + 0.6y = 3.8 (20)

Q. 3 (a) A company is considering two products Type I and type II. Type I requires Ό hours on a drill and 1/8 hours on a lathe. Type II requires ½ hours on a drill and Ύ hours on a lathe. The profit from Type I is $50 per product, and the profit from Type II is $102 per product. If the machines are limited to 8 hours per day, how many of each product should be produced to maximize profit?

(b) Graph the following functions:

1. 2x2 y2 = 9 2. 3xy = 4 (20)

Q. 4 (a) Minimize 2y1 + 5y2 = C

Subject to:

3y1 + 2y2 ≥ 8

Y1 + 4y2 ≥ 6

Y1 ≥ 0

Y2 ≥ 0

(b) Solve the following system of equations by using the inverse matrix method:

2x + 4y = 10

3x 4y = 6 (20)

Q. 5 Find the payment needed each month to pay off a debt of $1000 at 12% interest compounded semi annually. (20)

ASSIGNMENT No. 2

(Units: 69) Total Marks: 100

Note: All questions are compulsory and carry equal marks.

Q. 1 There are six roads from A to B and four roads between B and C.

(a) In how many ways can the trip be made?

(b) In how many ways can she drive round trip from A to B to C and return to A through B.

(c) Prepare tree diagram to support your answer. (20)

Q. 2 Three manufacturing plants A, Z, and N supply respectively 60%, 10%, and 30% of all shock absorbers used by a certain manufacturer. Records show that the percentage of defective items produced by A, Z and N is 1%, 2%, and 3% respectively. What is the probability that a randomly chosen shock absorber installed by the manufacturer will be defective? (20)

Q. 3 (a) A nationwide promotion promises a first prize of $25000 two second prices of $5000 and four third prices of $1000. A total of 950000 persons enter the lottery. What is the expected value of the lottery if the lottery cost nothing to enter?

(b) Find the fixed probability vector for the matrix (20)

Q. 4 The probability of a person passing the test for a drivers license on the first try is 0.75. The probability that an individual who fails on the first test will pass on the second try is 0.80, and the probability that an individual who fails the first and second tests will pass the third time is 0.70. Find the probability that an individual

(a) fails both the first and second tests;

(b) will fail three times in a row;

(c) will require at least two tries to pass the test. (20)

Q. 5 (a) If a marginal revenue function is given by

MR = 8000 0.8x

Find the total revenue for a sale of 300 items. What is the maximum revenue?

(b) Evaluate the following definite integrals:

1. dx

2. dx (20)

BUSINESS MATHEMATICS

(Course Outline BBA-135)

Unit 1 Fundamental Concepts of Modern Mathematics

Introduction to Set Notation

The Real Numbers

Solution Sets for Equations and Inequalities

Graphs

Slopes and Linear Equations

Applications of Percentages in Business

Unit 2 Equations and Inequalities

Rectangular Co-Ordinates

The Straight Line

Solution of Linear Systems

System of Linear Equalizations and Matrices

Applications

Linear Inequalities

Quadratic Equations

Unit 3 Graphs and Functions

Exponents and Radicals

Concept of a Function

Basic Operations with Algebraic Expressions

Quadratic Functions and Quadratic Equations

Aids to Graphing Functions

Introduction to Graphs of Polynomial and Rational Functions

Exponential Functions

Logarithmic Functions

Unit 4 Introduction to Matrices with Application

Addition of Matrices

Matrix Multiplication

Row Operations

Inverse of a Matrix

Systems of m Equations in Unknowns

Application of Matrices in Business

Unit 5 Introduction to Linear Programming

Introduction to Linear Programming

Geometric Approach to Linear Programming

The Simplex Method

The Smilax Method of Maximization

Minimization Using the Dual Problem

Unit 6 Mathematics of Finance

Simple and Compound Interest

Discount

Geometric Progression and Annuities

Sinking Fund

Present Value of an Annuity; Amortization

Future Value of an Annuity; Sinking Funds

Leasing, Capital Expenditure

Unit 7 Probability and its Application

Permutations and Combinations

Experiments, Sample Spaces and Events

Properties of the Probability of an Event

Conditional Probability

Expected Value

Independent Events

Bayess Formula

The Binomial Probability Model

Unit 8 The Derivatives

The Concept of a Limit

Continuous Functions

The Average Rate of Change

Formulas for Derivatives

Relative Maxima and Relative Minima

Absolute Maximum and Absolute Minimum

Application of Derivatives in Business

Unit 9 Integration

The Indefinite Integral

Integration by Substitutions

Integration by Parts

Differential Equations

The Definite Integral

Application in Geometry: Area Under a Graph

Application in Business

______[]______

ALLAMA IQBAL OPEN UNIVERSITY ISLAMABAD

(Department of Business Administration)

BUSINESS MATHEMATICS (BBA-135)

(CHECKLIST)

SEMESTER: SPRING 2014

This packet comprises the following material:

1. Text Book (one)

2. Course Outline

3. Assignment No. 1 & 2

4. Assignment Forms (2 sets)

If you find anything missing out of the above-mentioned material, please contact at the address given below:

Mailing Officer

Mailing Section, Block No. 28

Allama Iqbal Open University

H-8, ISLAMABAD

Phone: 051-9057611-12

Course Coordinator

ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD

(Department of Business Administration)

WARNING

1. PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.

2. SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM OTHER(S) AS ONES OWN WILL BE PENALIZED AS DEFINED IN AIOU PLAGIARISM POLICY.

ASSIGNMENT No. 1

(Units: 15)

Course: Business Mathematics (135) Semester: Spring 2014

Level: BBA Total Marks: 100

Pass Marks: 40

Note: All questions are compulsory and carry equal marks.

Q. 1 (a) Let A={2,4,6,8,10], B={6,8,11,12} and U={1,2,3,4,5,6,7,8,9,10,11,12}

Find

(1) Ac (2) AB (3) (AB)c (4) AB

(b) A store manager plans to increase the selling price of an item by 7%. If the item costs $6.52 and presently sells for $8.95. How much increase in price occurs after the increase in selling price.

(c) Find the equation of a line containing the points (4, 7) and 3, 6). (20)

Q. 2 (a) A service industry Williamss system has the following input coefficient matrix.

Services

Manufacturing

Farming

If the demand from the consumer section are 21, 5 and 1 units respectively. Find the output needed for these demands.

(b) Find the solution set of the following equations:

1. 6x + 2y = 6 and 12x + 4y = 12

2. 0.02x 0.4y = 0.2; and 0.04x + 0.6y = 3.8 (20)

Q. 3 (a) A company is considering two products Type I and type II. Type I requires Ό hours on a drill and 1/8 hours on a lathe. Type II requires ½ hours on a drill and Ύ hours on a lathe. The profit from Type I is $50 per product, and the profit from Type II is $102 per product. If the machines are limited to 8 hours per day, how many of each product should be produced to maximize profit?

(b) Graph the following functions:

1. 2x2 y2 = 9 2. 3xy = 4 (20)

Q. 4 (a) Minimize 2y1 + 5y2 = C

Subject to:

3y1 + 2y2 ≥ 8

Y1 + 4y2 ≥ 6

Y1 ≥ 0

Y2 ≥ 0

(b) Solve the following system of equations by using the inverse matrix method:

2x + 4y = 10

3x 4y = 6 (20)

Q. 5 Find the payment needed each month to pay off a debt of $1000 at 12% interest compounded semi annually. (20)

ASSIGNMENT No. 2

(Units: 69) Total Marks: 100

Note: All questions are compulsory and carry equal marks.

Q. 1 There are six roads from A to B and four roads between B and C.

(a) In how many ways can the trip be made?

(b) In how many ways can she drive round trip from A to B to C and return to A through B.

(c) Prepare tree diagram to support your answer. (20)

Q. 2 Three manufacturing plants A, Z, and N supply respectively 60%, 10%, and 30% of all shock absorbers used by a certain manufacturer. Records show that the percentage of defective items produced by A, Z and N is 1%, 2%, and 3% respectively. What is the probability that a randomly chosen shock absorber installed by the manufacturer will be defective? (20)

Q. 3 (a) A nationwide promotion promises a first prize of $25000 two second prices of $5000 and four third prices of $1000. A total of 950000 persons enter the lottery. What is the expected value of the lottery if the lottery cost nothing to enter?

(b) Find the fixed probability vector for the matrix (20)

Q. 4 The probability of a person passing the test for a drivers license on the first try is 0.75. The probability that an individual who fails on the first test will pass on the second try is 0.80, and the probability that an individual who fails the first and second tests will pass the third time is 0.70. Find the probability that an individual

(a) fails both the first and second tests;

(b) will fail three times in a row;

(c) will require at least two tries to pass the test. (20)

Q. 5 (a) If a marginal revenue function is given by

MR = 8000 0.8x

Find the total revenue for a sale of 300 items. What is the maximum revenue?

(b) Evaluate the following definite integrals:

1. dx

2. dx (20)

BUSINESS MATHEMATICS

(Course Outline BBA-135)

Unit 1 Fundamental Concepts of Modern Mathematics

Introduction to Set Notation

The Real Numbers

Solution Sets for Equations and Inequalities

Graphs

Slopes and Linear Equations

Applications of Percentages in Business

Unit 2 Equations and Inequalities

Rectangular Co-Ordinates

The Straight Line

Solution of Linear Systems

System of Linear Equalizations and Matrices

Applications

Linear Inequalities

Quadratic Equations

Unit 3 Graphs and Functions

Exponents and Radicals

Concept of a Function

Basic Operations with Algebraic Expressions

Quadratic Functions and Quadratic Equations

Aids to Graphing Functions

Introduction to Graphs of Polynomial and Rational Functions

Exponential Functions

Logarithmic Functions

Unit 4 Introduction to Matrices with Application

Addition of Matrices

Matrix Multiplication

Row Operations

Inverse of a Matrix

Systems of m Equations in Unknowns

Application of Matrices in Business

Unit 5 Introduction to Linear Programming

Introduction to Linear Programming

Geometric Approach to Linear Programming

The Simplex Method

The Smilax Method of Maximization

Minimization Using the Dual Problem

Unit 6 Mathematics of Finance

Simple and Compound Interest

Discount

Geometric Progression and Annuities

Sinking Fund

Present Value of an Annuity; Amortization

Future Value of an Annuity; Sinking Funds

Leasing, Capital Expenditure

Unit 7 Probability and its Application

Permutations and Combinations

Experiments, Sample Spaces and Events

Properties of the Probability of an Event

Conditional Probability

Expected Value

Independent Events

Bayess Formula

The Binomial Probability Model

Unit 8 The Derivatives

The Concept of a Limit

Continuous Functions

The Average Rate of Change

Formulas for Derivatives

Relative Maxima and Relative Minima

Absolute Maximum and Absolute Minimum

Application of Derivatives in Business

Unit 9 Integration

The Indefinite Integral

Integration by Substitutions

Integration by Parts

Differential Equations

The Definite Integral

Application in Geometry: Area Under a Graph

Application in Business

______[]______