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
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