WELCOME TO OUR PRESENTATION

MATHEMATICS FOR BUSINESS DECISIONS

How Does Mathematics Assist In Decision Making

Presentation Topic:

SPECIAL THANKS TO

Kazi Md. Nasir UddinAssistance Professor

Department of Accounting & Information Systems

Faculty of Business StudiesJagannath University, Dhaka.

GROUP MEMBERS

Name ID No.

MD. FAHAD MIA B-120201028

MD.SHAMIM REZA B-120201029

MD. IFTEKHAR HASAN B- 120201031

AFROZA FAIRUZ B- 120201032

PRESENTATION TOPICS

Matrix

Coordinate geometry

Function, Limit & Continuity

Differentiation

MATHEMATICS AND BUSINESS DECISION

Presenter: MD. FAHAD MIA

ID- B-120201028

Presentation Topic:

Matrix

MATRIX

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

PRACTICAL USE OF MATRIX IN BUSINESS

MATHEMATICS AND BUSINESS DECISION

Presenter:SHAMIM REZAID- B-120201027

Presentation Topic: Coordinate Geometry

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.

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 yyxxpoMid

Distance between two points: The distance, say d, between two points P(x1, y1) and Q(x2, y2) is given by the formula:

222

212 )()( yyxxd

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.

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

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.

SOLUTION

MATHEMATICS AND BUSINESS DECISION

Presenter:

MD. Iftekhar HasanID- B-120201028

Presentation Topic: Function, limit and Continuty

FUNCTION

Function is a technical term that is used to symbolize the relationship between two variables.

Y = f (x) = x + 2

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

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

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

MATHEMATICS AND BUSINESS DECISION

Presenter:

Afroza Fairuz

ID- B- 120201032

Presentation Topic: Differentiation, Maxima & Minima

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,

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

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.

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.

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..