The presentation discusses how mathematics, including matrices, coordinate geometry, functions, limits, continuity, differentiation, and maxima and minima, can assist in business decision making. Several group members each presented on a mathematics topic and provided examples of how it is used, such as using matrices to analyze production elements or differentiation to determine optimal production levels for maximizing profit. The document concludes by solving an example maximizing profit by finding the production rate that balances total cost and total revenue functions.

1. WELCOME
TO OUR
PRESENTATION

2. MATHEMATICS FOR BUSINESS
DECISIONS
How Does Mathematics Assist In Decision Making
Presentation Topic:

3. SPECIAL THANKS TO
Kazi Md. Nasir Uddin
Assistance Professor
Department of Accounting & Information Systems
Faculty of Business Studies
Jagannath University, Dhaka.

4. GROUP MEMBERS
Name ID No.
MD. FAHAD MIA B-120201028
MD.SHAMIM REZA B-120201029
MD. IFTEKHAR HASAN B- 120201031
AFROZA FAIRUZ B- 120201032

5. PRESENTATION TOPICS
 Matrix
 Coordinate geometry
 Function, Limit & Continuity
 Differentiation

6. MATHEMATICS AND BUSINESS DECISION
 Presenter:
MD. FAHAD MIA
ID- B-120201028
Presentation Topic:
Matrix

7. MATRIX

8. THINGS YOU CAN DETERMINE THROUGH MATRIX
 Analyze the elements production
 Determine equilibrium price and quantity in perfect
competitive market
 Determine the maximum profit indicator production
 Determine the allocation of expenses
 Budget for by products
 Determine the input and output tables
 Study of inter-industry economics

9. PRACTICAL USE OF MATRIX IN BUSINESS

14. MATHEMATICS AND BUSINESS DECISION
Presenter:
SHAMIM REZA
ID- B-120201027
Presentation Topic:
Coordinate Geometry

15. COORDINATE GEOMETRY
 A system of geometry where the position of points
on the plane is described using an ordered pair of
numbers.
Quadrants: The two directed lines, when they intersect at
right angles at the point of origin, divide their plane into
four parts or regions. These four parts are known as
quadrant.
Coordinates: In a two dimensional figure, a point in plane
has two coordinates. The first coordinate is known as x-
coordinate and second coordinate is known as y-
coordinate.

16. Coordinates of mid point: We can find out the coordinates of a
mid point from the coordinates of any two points using the following
formula:





 

2
,
2
:int 1212 yyxx
poMid
Distance between two points: The distance, say d, between
two points P(x1, y1) and Q(x2, y2) is given by the formula:
2
22
2
12 )()( yyxxd 

17. THINGS YOU CAN DO IN COORDINATE
GEOMETRY
If you know the coordinates of a group of points you
can:
 calculate the midpoint of a line segment.
 plot points the points
 calculate the distance between two points.
 calculate the median and mean of a data set.
 describe how mathematical modeling can be used
in decision making.

18. THINGS YOU CAN DO IN COORDINATE
GEOMETRY
 give a criterion function, using a simple
mathematical model to assist in decision making.
 define appropriate data structures
 read and display external data files
 design and implement computer program for use in
business planning

19. FOR EXAMPLE:
 The following grid represents the streets and
houses of Simpletown. The mayor is trying to
determine the best place to build the rescue squad.
This town has only two houses. On the town grid,
the Adams are located at A(2,3) and the Browns are
located at B(6,-4).
 Objective: Determine the Ideal location “K” for
the rescue squad.

20. SOLUTION

21. MATHEMATICS AND BUSINESS DECISION
 Presenter:
MD. Iftekhar Hasan
ID- B-120201028
Presentation Topic:
Function, limit and Continuty

22. FUNCTION
Function is a technical term that is used to symbolize the
relationship between two variables.
Y = f (x) = x + 2

24. THINGS YOU CAN DO THROUGH FUNCTION
 You can find out the relationship between two real
variables.
Such as:
 You can find out the relationship between cost and revenue
 You can find out the distance through a function of time and speed
 You can find out the relation between Time and Labor
 You can Find out the relationship between Time and units of production
 You can find out the profit through a function of loss
 You can find out the quantity demanded with a function of price

25. Limit : The limit of a function is that fixed value to which a
function approaches as the variable approaches a given value. The
function approaches this fixed constant in such a way that the
absolute value of the difference between the function and the constant
may be made smaller and smaller than any positive number, however
small.
Continuity: A function f(x) is said to be continuous at x=a, if
corresponding to any arbitrarily assigned positive number,
however small there exists a positive number

26. PRACTICAL EXAMPLES OF FUNCTION:
 Distance covered is a function of time and speed
 The railway freight changed is a function of weight
or volume
 The quantity demanded is a function of price
 The product supplied is a function of demand

27. MATHEMATICS AND BUSINESS DECISION
 Presenter:
Afroza Fairuz
ID- B- 120201032
Presentation Topic: Differentiation,
Maxima & Minima

28. DIFFERENTIATION
 Differentiation is the process of finding slopes of
tangents to the graph of a given function.
 Differentiation is the process of finding out the derivative
of a continuous function. A derivative is the limit of the
ratio of the increment in the function.
If the increment is very small, near to zero we can say,

29. DIFFERENTIATION IN BUSINESS DECISION
MAKING
 With the increasing in use of quantitative techniques in
business, there is increasing use of calculus based
quantitative models. Such models are used in production
& operations of business.
 It is also an essential tool in the study of optimization
 It helps to determine the maxima & the minima of
functions.
 It is an important tool for finding out the minimum &
maximum cost or profit of a manufacturing company.
 We can find out demand & supply function in economics

30.  Definition:
Maxima and minima of a function are the largest and
smallest value that the function takes at a point either
within a given neighborhood or on the function domain.
Maxima: A function is said to have attained its maximum
value at x=a, if the function ceases to increase and begins
to decrease at x=a.
Minima: A function is said to have attained its minimum
value at x=b, if the function ceases to decrease and then
begin to increase at x=b.

31. APPLICATION OF MAXIMA AND MINIMA
1.In chemistry, we have used the maxima and the minima
to determine where an electron is most likely to be found in
any given orbital.
2. In Economics maxima and minima are used to maximize
beneficial values and to minimize negative ones. A
meteorologist creates a model that predicts temperature
variance with respect to time.

32. EXAMPLE:
 A company has examined its cost and revenue
structure and determined that total cost C and total
revenue R and total output X are related as:
C = 1000 + 0.0015 x2
And, R = 3x
Find the production rate x that will maimize the profit of the
company..