WELCOME TO CA’ FOSCARI, WELCOME TO VENICE. WELCOME TO CA’ FOSCARI.
Welcome
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Transcript of Welcome
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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
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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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Production in each land
Firm-1 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 MatrixTo 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?
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Tabulate the data as follows
VITAMIN
P Q R REQUIREMENT
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 =
Here the determinant of A │A│ =
= 2=4-5 = 1
223
232
121
223
232
121
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M =
=
32
21
22
11
23
1223
21
23
11
22
1223
32
23
22
22
23
Here the minor matrix,
101
412
522
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Here Adjoint Matrix,
A =
A-1 = .AdjA
=
145
012
122
A
1
145
012
122
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z
y
x
=
145
012
122
×
13
14
8
=
3
2
1
=
135640
01416
132816
Putting the value in the equation
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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
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)
200
11.10
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Graph
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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-2SoundTech, 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
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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.
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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.
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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.
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Parts of an AnnuityParts of an Annuity
0 1 2 3
$100 $100 $100
(Ordinary Annuity)EndEnd of
Period 1EndEnd of
Period 2
Today EqualEqual Cash Flows Each 1 Period Apart
EndEnd ofPeriod 3
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Parts of an AnnuityParts of an Annuity
0 1 2 3
$100 $100 $100
(Annuity Due)BeginningBeginning of
Period 1BeginningBeginning of
Period 2
Today EqualEqual Cash Flows Each 1 Period Apart
BeginningBeginning ofPeriod 3
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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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FindingsMatrix 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