Transcript File

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Welcome
Use of
mathematical
tools in business
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Prepared for
Farzana Lalarukh
Assistant professor, Department of Finance
Faculty of Business Studies
University of Dhaka
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We are
SL
01
02
03
04
05
NAME
Shyamal Biswas
Md. Mosarraf Hossain
Md. Sohel Rana
Sanjib Shil
S. M. Toha Salim
ROLL
15-015
15-033
15-101
15-103
15-145
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Agenda
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Measuring GDP in the product
approach using matrix
• GDP is the market value of all final goods and
services made within the borders of a country in
a year.
GDP can be determined in three ways,
1) the product (or output) approach,
2) the income approach, and
3) The expenditure approach.
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Assumptions
• There are only two firms in Bangladesh
• A firm consists of three lands
• Paddy and wheat are produced by two firms
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Firm-1
Production in each land
Firm-2
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Measuring procedure
• Total production from all firms is calculated
• GDP=Total production
Market Price
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Summation
Total Production
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So the GDP is 40+60+64=164 taka
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Case Analysis Using Inverse Matrix
To produce PRAN MANGO JUICE it is necessary to use
 8 units of vitamin A, 14 units of vitamin B, and 13 units
of vitamin C.
 One tube of mixture P contains 1 unit of A, 2 units of B
and 3 units of C.
 One tube of mixture Q contains 2 units of A, 3 units of
B, and 2 units of C.
 One tube of mixture R contains one unit of A, 2 units of
B, and 2 units of C.
How many tubes of each type of mixture should be
used to produce the juice?
Tabulate the data as follows
V
I
T
A
M
I
N
P
Q
R
REQUI
REMEN
T
A
1
2
1
8
B
2
3
2
14
C
3
2
2
13
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Let x tubes of P, y tubes of Q and Z tubes of R be used
to produce the juice. Then
x+2y+z=8
2x+3y+2z=14
3x+2y+2z=13
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Writing the equations in the matrix form
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We can solve the problem by the inverse of a matrix
Let
A =
1
2
3
2
3
2
1
2
2
Here the determinant of A
1
│A│ = 2
3
= 2=4-5
= 1
2
3
2
1
2
2
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Here the minor matrix,
M=
3

2
2

2
2

3
2
= 2
1
2
2
1
2
1
2
2
3
1
3
1
2
2
2
1
2
1
2
2
1
0
2
3
1
3
1
2
3

2
2

2
2

3 
5
4
1
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Here Adjoint Matrix,
A=
A-1
2
2
5
2
1
4
1
0
1
1
=
.AdjA
A
=
2
2
5
2
1
4
1
0
1
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Putting the value in the equation
x
y
z
=
2 2 1
8
2  1 0 × 14
 5 4 1
13
=
16  28  13
16  14  0
 40  56  13
=
1
2
3
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Hence
 1 tube of mixture P,
 2 tubes of mixture Q,
 3 tubes of mixture R ,
should be used to produce the juice.
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Hence
 1 tube of mixture P,
 2 tubes of mixture Q,
 3 tubes of mixture R ,
should be used to produce the juice.
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What is Cost Function
 Cost function is a mathematical system relating a firms
total cost to its output.
TOTAL COST=
(VARIAVLE COST x OUTPUT)
(+) FIXED COST
 It is also a relationship between activity and its cost.
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Who use it
 Manufacturer company,
 Service company such as gas, electricity,
 Oil company,
 Many other small organizations.
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Case analysis
 General Electronics Company(GEC) charges its
customers according to their usage of electricity
and follows a fixed cost of 3.35 taka and 3.380
paisa per unit for the first 350 unit,5.634 paisa per
unit in excess of 350.
 The requirements are finding out cost function,
graph, total and average cost of using 200 units.
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Case analysis (cont’d)
For first 350 units
C(k)=3.35+0.0338k
Total cost of using 200units:
C(200)=3.35+0.0338(200)
=10.11 taka
10.11
200
Average cost=
=0.05055
In excess of 350 units
C(350)=3.35+0.0338(350)
C=15.18
SO,
C(k)=15.18+0.5634(k-350)
Graph
Break even analysis
• Break even point is the point where total
revenue is equal to the total cost, that is,
profit=0
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Case analysis-2
SoundTech, a manufacturer of compact disc (CDs) has
 a fixed cost of 1000 Taka
 variable cost of 7 Taka
 Selling price is 12 Taka per CD.
 A) find the revenue, cost and profit function?
a)R(q) =12Q
C(q) =7Q+10000
P(q) =12Q-(7Q+10000)
= 5Q-10000
 b) What is the profit if 2800 CDs are made and sold?
b)P(2800) =5(2800)-10000
=4000
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 c) What is the profit if 1000 CDs are made and sold?
c) P(1000) =5(1000)-10000
= -5000
 d) At What no. Of CDs made and sold will manufacturer
break even?
d) Break even point: 5Q-10000=0
Q=2000 CDs
 e) At what sales volume (revenue) will break even occurs?
e) Break even dollar volume of sales:
R(2000) =12(2000)
= 24000 Taka
Graph
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Time value of money
• Present value is the
current worth of a
future sum of money
given a specified rate
of return.
• Future value is the
value of an asset or
cash at a specified
date in the future.
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Annuity
• An annuity is an amount of money that occurs
(received or paid) in equal amounts at equally
spaced time intervals.
• These occur so frequently in business that
special calculation methods are generally used.
Example of present value
• Sanjib is planning to buy a car
next year that will cost taka
40,000 at that time. If the
interest rate is 13% how much
should he set aside now and to
deposit in a bank in order to
pay for the purchase?
•
So he should set aside now and to
deposit in a bank taka 35,398.23 in
order to pay for the purchase.
Example of Future Value
• Shamim places taka
10,000 in a savings
account @ 13% interest
compounded annually.
How much will he get at
the end of 5 years?
• He will get taka 11592.74 at
the end of 5 years.
FV=PV(1=i)n
FV=10,000(1+1.13)5
FV=11592.72
Parts of an Annuity
(Ordinary Annuity)
End of
Period 1
0
Today
End of
Period 2
End of
Period 3
1
2
3
$100
$100
$100
Equal Cash Flows
Each 1 Period Apart
Parts of an Annuity
(Annuity Due)
Beginning of
Period 1
Beginning of
Period 2
0
1
2
$100
$100
$100
Today
Beginning of
Period 3
3
Equal Cash Flows
Each 1 Period Apart
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Present Value of Annuity
• Selim took a loan of taka 15,00,000 from Brac
Bank at 15% interest to be repaid in equal yearly
installment over next 20 years.
• What will be his annual payment at the beginning
of each year?
• What will be his annual payment at the end of
each year?
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Findings
 Matrix is used to calculate large amount of data
in a simple and smarter way.
 Cost function and break even point analysis help
to find marginal cost, marginal revenue and
optimum level of production.
 Interest on loan/deposit, amount of annuity etc
are easily calculated by using time value of
money concept.
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ANY
QUEARY?
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THANKS TO
ALL