Lec 4 BBA1 Sunday

Lecture 4
Business Mathematics and

Statistics
Dr. Muhammad Arif Hussain

Today’s Topics
• Application of linear equations

• Simultaneous equations
Graphical Representation of Part (d)
Determining the equation of a straight line
Given a non-vertical straight line with slope m

and containing the point (x1, y1), the slope of
the line connecting (x1, y1) with any other
point (x, y) is given by
Rearranging gives: y-y1 = m(x-x1)

Example
Find the equation of line having slope m = −2 and
passing through the point (2, 8).
Book by BUDNICK P 58
y  y1  mx  x1 
Considering the linear equation 3x - 6y = 24;

(a) What is the slope of the line?
(b) What is the slope of any line parallel to the given line?
(c) What is the slope of any line perpendicular to the given
line?
(d) How many different lines are perpendicular to this line?
(e)Find the equation of the line which is perpendicular to the
given line and which passes through the point (2, 5).
Solution SLOPE FORMULA : m
y2  y1
x2  x1
PARALLEL LINES : m1 = m2
PERPENDICULAR LINES: m1 m2 = 1
SLOPE-INTERCEPT FORM: y  mx  b
point-slope form y  y1  mx  x1 

Ex 2.3
Ex 2.3
The book value of a machine is expressed by the equation V = 60,000 – 7,500 t
Where V equals the book value in dollars and t equals the age of the machine expressed
in years.
(a) Identify the t and V intercepts.
(b) Interpret the meaning of the intercepts.
(c) Interpret the meaning of the slope.
(d) Sketch the function.
• Solve problems
• (SAT Scores) One small college has observed a downward
trend in the average SAT score of applicants to the college.
Analysis has resulted in the equation s = 620 – 4.5 t
• Where s equals the average SAT score for a given year and t
equals the time measured in years since 1985 (t = 0)
• (a) Identify s and t intercepts.
• (b) Interpret the meaning of the intercepts.
• (c) Interpret the meaning of the slope.
• (d) Sketch the equation.
Linear cost function:
The organizations are concerned with the costs as they
reflect the money flowing out of the organisation. The
total cost usually consists of two components: total
variable cost and total fixed cost. These two
components determine the total cost of the organisation .
Total cost function = total variable cost + total fixed cost

Basic Business Applications.
Cost Function C = Unit cost ·
Quantity + Fixed cost Where m (slope) is the
unit cost and b (the y-intercept) is the fixed cost.
Revenue Function R = (price) ·

(quantity sold) (Note: quantity is number of
items sold at price of $p.)
16
Linear Profit function:
•If total revenue exceeds total cost the profit is positive

•In such case, profit is referred as net gain or net profit
•On the other hand the negative profit is referred to as a net loss or net deficit.
Example: Break-Even Analysis
A recording company produces compact disk (CDs).

One-time fixed costs for a particular CD are $24,000;
this includes costs such as recording, album design,
and promotion. Variable costs amount to $6.20 per
CD and include the manufacturing, distribution, and
royalty costs for each disk actually manufactured and
sold to a retailer. The CD is sold to retail outlets at
$8.70 each. How many CDs must be manufactured
and sold for the company to break even?
Break-Even Analysis
(continued)
Solution
Step 1. Let x = the number of CDs manufactured and sold.

Step 2. Fixed costs = $24,000
Variable costs = $6.20x
C = cost of producing x CDs
= fixed costs + variable costs
= $24,000 + $6.20x
R = revenue (return) on sales of x CDs
= $8.70x
Break-Even Analysis
(continued)
Step 3. The company breaks even if R = C, that is if

$8.70x = $24,000 + $6.20x
Step 4. 8.7x = 24,000 + 6.2x Subtract 6.2x from both sides
2.5x = 24,000 Divide both sides by 2.5
x = 9,600
The company must make and sell 9,600 CDs
to break even.
Simultaneous Equations
Solution to a System of Equations
Determine whether the ordered pair (5, 1)
is a solution to the given system of equations.
Solving Systems of Linear Equations by Graphing
Solve the system of equations by graphing
 y3 

 y  4 x  1
Solution :  1,3
33 3  4  1  1
33
Mini-Project
Submit by Nov 03, 2019
Total marks = 15 = 7 (report) + 8 (presentation)
n = your serial number in attendance sheet
Final marks will be decided after the

presentation given by each student.

Mini-Project

Open code
Q1. Obtain derivative of f(x) = n* x^n up to fifth order.

Where n = your serial number in attendance sheet
Q2. Obtain results of Q1using computer program.
Q3. Obtain integral of f(x) = n* x^n

Manually and using computer program.
Q4. Find inverse of
Q5. Obtain results of Q4 using computer program.

Mini-Project
Q6. A firm determines that x units of its product can be sold daily
at p dollars per unit, where .x  1000  p The cost of producing x units per
day is C ( x )  3000  20 x . Find the revenue and profit functions.
Assuming that the production capacity is at most 500 units per day,
determine how many units the company must produce and sell each
day to maximize profit.
Find the maximum profit. What price per unit should be charged
to obtain maximum profit?.
Q7. Solve the system of equations Qs. 1, 2, 3 of Ex: 3.2

manually and using computer application.
Q8. Prepare a report to explain the results of Q1 and Q7.

Lec 4 BBA1 Sunday

Uploaded by

Copyright:

Available Formats

Lec 4 BBA1 Sunday

Uploaded by

Document Information

Original Description:

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Lec 4 BBA1 Sunday

Uploaded by

Copyright:

Available Formats

Lecture 4

Business Mathematics and

Dr. Muhammad Arif Hussain

• Application of linear equations

Given a non-vertical straight line with slope m

Rearranging gives: y-y1 = m(x-x1)

Considering the linear equation 3x - 6y = 24;

point-slope form y  y1  mx  x1 

Total cost function = total variable cost + total fixed cost

Revenue Function R = (price) ·

•If total revenue exceeds total cost the profit is positive

A recording company produces compact disk (CDs).

Step 1. Let x = the number of CDs manufactured and sold.

Step 3. The company breaks even if R = C, that is if

Solve the system of equations by graphing

Total marks = 15 = 7 (report) + 8 (presentation)

n = your serial number in attendance sheet

Final marks will be decided after the

Q1. Obtain derivative of f(x) = n* x^n up to fifth order.

Q2. Obtain results of Q1using computer program.

Q3. Obtain integral of f(x) = n* x^n

Q5. Obtain results of Q4 using computer program.

Q7. Solve the system of equations Qs. 1, 2, 3 of Ex: 3.2

Q8. Prepare a report to explain the results of Q1 and Q7.

You might also like