Business Mathematics is mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.

4. EMRAN HOSAIN
ID No. M18150203721
KHADIZA AKTER
ID No. M18150203710
APU GOSH
ID No. M18150203713
RABYA BEGUM
ID No. M18150203703
A. B. M FAZLA MUKITH KHAN
ID No. M18150203746
MD. Hasan Imam
ID No. M18150203745

5. Application of Business Mathematics

6. Business Mathematics is mathematics used by commercial enterprises to
record and manage business operations. Commercial organizations use
mathematics in accounting, inventory management, marketing, sales
forecasting, and financial analysis.
Business Mathematics

7. Number System
A number system is a writing system for expressing numbers; that is, a mathematic notation for
representing numbers of a given set, using digits or other symbols in a consistent manner.

8. A set is a group or collection of objects or numbers, considered as an entity unto itself.
A Survey on Consumer Preference
A question was Asked 1200 consumers, that which company’s transportation do you prefer And provide
them 3 alternatives: Uber, Pathao and Amar Ride. Among Them 512 chose Uber, 600 chose Pathao and
350 chose Amar-Ride. 195 chose both Uber & Pathao, 122 chose both Uber & Amar-Ride, 150 chose
Pathao & Amar-Ride and 50 chose all of them. Now from Above data we can determine:
1. How Many consumer did not Choose any one?
2. How Many consumers choose only one?
Set

9. Venn Diagram of Consumer Preference
Only Uber Users
Only Pathao users
Only Amar-Ride users
Both Uber & Pathao users
Both Pathao & Amar-Ride users
Both Uber & Amar-Ride users
All three of them users
Consumer use None of this
Uber
Pathao Amar-Ride
Non-users
195
305
128
245
150
122
50
155

10. A linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the
equation results in a straight line.
y=mx + b
Example:
Uber-XL initial cost is 100Tk. & cost per km. is 32Tk. Therefore, Uber-XL’s total cost linear equation is
y=32x + 100
Assume that, Uber-XL’s per km. earning is 52.00 Tk.
Therefore, Uber-XL’s total Revenue function is, R=52x
Uber-XL’s profit function is, P = R – y
P = 52x – 32x – 100
P = 20x - 100

11. Break Even Point
Uber-XL’s Break-Even Quantity-
Where, P= 0
or, 20x – 100 = 0
or, 20x = 100
or, x = 100/20
or, x = 5 km.
Uber-XL’s Break-Even Revenue or Price-
Where, R= 52 X 5
or, R = 260 100
260
50 Quantity(km.)
Revenue/Price(Tk.)
VariableCost
} Fixed Cost
Figure: Break Even Point Analysis of a Uber-XL

12. Quadratic Equation
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is
squared.
ax² + bx + c = 0
Uber-XL’s total Cost function is y =32x + 100
Uber-XL’s total Revenue function is R = -0.26x² + 84x
Therefore, The profit function will be,
P= (-0.26x² + 84x) – (32x + 100)
P = -0.26x²+ 52x - 100

13. Quantity
(Hours)
x
P = - 0.26𝒙 𝟐
− 100x - 100
0 -100
1 -48.26
2 2.96
3 55.66
4 103.84
5 153.5
99 2499.74
100 2500
101 2499.74
198 2.96
199 -48.26
200 -100 -1000
-500
0
500
1000
1500
2000
2500
3000
0
9
18
27
36
45
54
63
72
81
90
99
108
117
126
135
144
153
162
171
180
189
198
207
TotalCost(Tk.)
Quantity (km.)
P = -0.26X² + 100X - 100
(100 , 2500)

14. Progression
An arithmetic progression (AP) is a sequence of numbers such that the common difference between any
two succeeding numbers is constant.
A Uber-Xl’s ride cost a customer initially Taka 100 and per Taka 32 for per km. So, first kilometer cost Taka 132
and next subsequent kilometer would cost Taka 32. That will create a arithmetic progression series like,
132, 164, 196, 228, 260, …………
The nth term of AP series is = a+(n-1)d
Where, Passing distance in kilometer = n
First term, a = 132
The common difference, d = 164 – 132 = 32
Arithmetic Progression

15. Geometric Progression
A sequence of terms in which the ratio between any two successive terms is the same.
Example:
A Uber-Xl’s driver open a Fixed Deposit account of Tk. 1,00,000 for 20 years in Bank Asia. Where he will get
10% compound interest. The interest of that deposit will create a geometric progression series like,
10000, 11000, 12100, 13310, 14641, ……….
The nth term of GP series is = ar(n-1)
Where, Number of years = n
First term, a = 10000
The common ratio is, r = 11000 / 10000 = 1.1

17. Matrix
A matrix is a collection of numbers arranged into a fixed number of rows and columns.
Usually the numbers are real numbers.
Data Organization
Matrices can also be used to organize information so it’s easy to read.
When you do this, it is kind of like making a miniature spreadsheet.

18. Moto Intercity XL Premier
Fall 52 24 16 11
Winter 37 31 28 18
Spring 48 26 19 17
Summer 61 38 22 20
Total rent service provided in 2018 by Uber (Thousand km.)

19. Matrices can be used to analyze different business situation
BCG Growth–Share Matrix

21. A coordinate geometry is a branch of geometry where the position of the points on the plane
is defined with the help of an ordered pair of numbers.
All of us use Apple or Google Maps every day to navigate and commute.
We see the graph like lines before loading the maps.

22. Global Positioning System (GPS)
Distance between two points P(x1, y1) and Q(x2, y2) is
given by:
The calculated flying distance from Dhaka to
Chittagong is equal to 131 miles which is equal to 211
km
(23.7104, 90.4074)
(22.3384, 91.8317)