Maths Revisd Ppt

8/14/2019 Maths Revisd Ppt

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URU NANAK

HALSA COLLEGE

A PROJECT ONQUANTITATIVE METHODS

FOR BUSINESS - II

Prepared By-

Group No 6


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ssignmentProblem


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Q. A company has 4 machines on which to do 3 jobs. Each job can be assigned to one and onlyone machine. The cost of each machine is given

in the following table:JOBS MACHINES

W X Y Z

A 18 24 28 32

B 8 13 17 19

C 10 15 19 22


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SOLUTION:

JOBS MACHINES

W X Y Z

A 18 24 28 32

B 8 13 17 19

C 10 15 19 22

D 0 0 0 0

Step 1: Introduce a dummy row


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Step 2: Subtract each element ofrow with the lowest element of

that rowJOBS MACHINES

W X Y ZA 18 24 28 32

B 8 13 17 19

C 10 15 19 22

D 0 0 0 0


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JOBS MACHINES

W X Y Z

A 0 6 10 14

B 0 5 9 11

C 0 5 9 12

D 0 0 0 0


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Step 3: Subtract each element of

column with the lowest element of thatcolumnJOBS MACHINES

W X Y ZA 0 6 10 14

B 0 5 9 11

C 0 5 9 12

D 0 0 0 0


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JOBS MACHINES

W X Y Z

A 0 6 10 14

B 0 5 9 11

C 0 5 9 12

D 0 0 0 0


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JOBS MACHINES

W X Y Z

A 0 6 10 14

B 0 9 11

C 0 5 9 12

D 0 0 0 0

Step 4: Draw minimum number oflines covering all the zeros.

5


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JOBS MACHINES

W X Y Z

A 0 1 5 9

B 0 0 6

C 0 0 4 7

D 5 0 0 0

Step 5: Number of lines drawn is

less than the order of matrix

4


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JOBS MACHINES

W X Y Z

A 0 1 1 5

B 0 0 0 2

C 0 0 0 3

D 9 4 0 0

Step 6: Since the number of linesdrawn is equal to the order of matrix


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JOBS MACHINES

W X Y Z

A 0 1 1 5

B 0 0 0 2

C 0 0 0 3D 9 4 0 0


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JOBS MACHINES

W X Y Z

A 1 1 5

B 0 0 2

C 0 0 3D 9 4 0 0

18

13

19


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The optimal assignment is -

JOBS MACHINES COST

A W 18

B X 13

C Y 19

TOTAL 50


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inancial-athematics I


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Q. Mr. Shahid has Rs. 10,000 and wantsto invest his money for 5 years to earnhigher returns on it. The bank providesinterest at the rate of 10% p.a. He isgiven a choice between two types ofinterest, which will he choose (whereinterest is compounded quarterly)?


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SOLUTION:

Here,

Principal (P) = Rs.10,000

Rate of interest(r) = 10% = 0.10

Number of years (n) = 5 years


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In Case of Simple Interest:

Simple Interest = P*n*r= 10000*5*0.10

= 5000Amount Realized (A) = Principal + S I

= 10000 + 5000= 15000

.. . Amount Realized = Rs. 15,000


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In Case of compound interest:

Number of times interest compounded (m) = 4

.. . Amount Realized (A) = 10000 (1+0.10)4*54

= 10000 (1+0.025)20

.. . Amount Realized (A) = 10000 (1.025) 20

Let x = 1.025 20


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Taking log on both the sides,

.. . log x = log (1.025)20

log x = 20.log (1.025)

log x = 20 (0.0107)

.. . log x = 0.214


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Taking antilog on both the sides,

antilog (log x) = antilog (0.214)

.. . X = 1.637

Amount Realized = 10000 * (1.637)

.. . Amount Realized = Rs. 16,370


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Type ofInterest

Principal plus interestearned

Simple Interest = 10,000 + 5,000= 15,000

Compound

Interest

= 10,000 + 6,370

= 16,370


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Q. What effective rate will bestated if an amount is deposited in a

bank for 1 year which yield anannual rate of 6% when compoundedsemi-annually?


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SOLUTION :

Here,

Rate of interest (r) = 6% = 6 = 0.06

100 Number of times interest compounded

(m) = 2

Number of years (n)= 1


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Since,

Effective Rate (r e) = ( 1+ r )m - 1m.. . r e = (1+0.06/2) 2 -1

= (1+0.03)2-1

.. . r e = (1.03)2 -1 = 1.0609 1

= 0.0609


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Converting into percentage,

r e = 0.0609 * 100

.. . r e = 6.09 %

..

. The Effective Rate is 6.09%


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THANK YOU

Maths Revisd Ppt

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