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Sl. No. Description Quantity Rate Amount Discount 1 Discount 2
1 Refrigerator 2 24200 48400 200 2420
2 Television 2 26700 53400 200 2670
3 Iron 3 1600 4800 200 240
4 Water Filter 5 3600 18000 200 900
5 Electric Fan 6 1400 8400 200 4206 Electric Bulb 25 22 550 200 27.5
1005, CDA Avenue East
Cash Memo
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Discount 3 Discount 4 Total Discount Total
2420 2420 7460 40940
2670 5340 10880 42520
0 48 488 4312
900 900 2900 15100
0 84 704 76960 0 227.5 322.5
Grand Total 110890.5
.
Nasirabad,
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SL. NO. Name Basic Pay H. RentMedical
Allowance
Conveyance
AllowanceTotal Pay
1 Sharif 4000 2200 400 500 71002 Salam 6400 2880 400 800 10480
3 Hamid 4500 2475 400 500 7875
4 Karim 7200 2880 400 800 11280
5 Nasim 5500 2750 400 500 9150
6 Sadia 6600 2970 400 800 10770
7 Kanti 7500 3000 400 800 11700
8 Kamal 5200 2600 400 500 8700
SL. NO. Name Performance Basic PayPerformance
AllowanceConveyance Total Pay
1 PANNA Excellent 7,500.00 4,000.00 500.00 12,000.00
2 LATIF Very Good 6,400.00 3,000.00 500.00 9,900.00
3 ISMAIL Poor 4,500.00 0.00 600.00 5,100.00
4 BABLU Average 7,200.00 1,000.00 500.00 8,700.00
5 KLHALED Good 5,500.00 2,000.00 600.00 8,100.00
6 CHAITY Average 6,600.00 1,000.00 500.00 8,100.00
7 PANTHO Excellent 4,000.00 4,000.00 600.00 8,600.00
8 JAMIL Good 5,800.00 2,000.00 600.00 8,400.00
Example 2
Example 1
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G.P.F. G. Insurance W. FundTotal
DeductionNet Pay
80 100 50 230 6870128 150 50 328 10152
90 100 50 240 7635
144 150 50 344 10936
110 150 50 310 8840
132 150 50 332 10438
150 150 50 350 11350
104 150 50 304 8396
G.P.F. G. Insurance W. FundTotal
DeductionNet Pay
150.00 150.00 50.00 350.00 11,650.00
128.00 150.00 50.00 328.00 9,572.00
90.00 100.00 50.00 240.00 4,860.00
144.00 150.00 50.00 344.00 8,356.00
110.00 150.00 50.00 310.00 7,790.00
132.00 150.00 50.00 332.00 7,768.00
80.00 100.00 50.00 230.00 8,370.00
116.00 150.00 50.00 316.00 8,084.00
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Acquisition Cost
Residual Value
Estimated Life Year
Year 1 2
Straight Line Depriciation (SLN) $2,400.00
Fixed Declining Balance Method (DB) $5,937.50 $3,117.19
Double Declining Balance Method (DDB) $5,000.00 $3,000.00
Sum-of-the Years Digit Method (SYD) $4,000.00 $3,200.00
Acquisition Cost
Residual Value
Estimated Life Year
Year 1 2
Straight Line Depriciation (SLN) $11,400.00
Fixed Declining Balance Method (DB) $23,625.00 $14,765.63
Double Declining Balance Method (DDB) $25,200.00 $15,120.00
Sum-of-the Years Digit Method (SYD) $19,000.00 $15,200.00
Acquisition Cost
Residual Value
Estimated Life Year
Year 1 2
Straight Line Depriciation (SLN) $84,000.00
Example 1
Example 2
Delta Company
Date: February, 2004
Example 3
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Fixed Declining Balance Method (DB) $227,470.00 $107,138.37
Double Declining Balance Method (DDB) $172,000.00 $103,200.00
Sum-of-the Years Digit Method (SYD) $140,000.00 $112,000.00
Acquisition Cost
Residual Value
Estimated Life Year
Year 1 2
Sum-of-the Years Digit Method (SYD) $147,142.86 $122,619.05
Acquisition Cost
Residual Value
Estimated Life Year
Year 1 2Double Declining Balance Method (DDB) $130,000.00 $78,000.00
Acquisition Cost
Residual Value
Estimated Life Year
Year 1 2
Double Declining Balance Method (DDB) $22,250.00 $16,687.50
Agro Indutries
Date: April, 2004
Exa
Example 5
Example 4
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3 4 5
$1,636.52 $859.17 $451.07
$1,800.00 $1,080.00 $648.00
$2,400.00 $1,600.00 $800.00
3 4 5
$9,228.52 $5,767.82 $3,604.89
$9,072.00 $5,443.20 $2,164.80
$11,400.00 $7,600.00 $3,800.00
3 4 5
5
500
12500
63000
6000
5
430000
10000
5
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$50,462.17 $23,767.68 $11,194.58
$61,920.00 $37,152.00 $22,291.20
$84,000.00 $56,000.00 $28,000.00
3 4 5 6
$98,095.24 $73,571.43 $49,047.62 $24,523.81
3 4 5$46,800.00 $28,080.00 $16,848.00
3 4 5 6 7 8
$12,515.63 $9,386.72 $7,040.04 $5,280.03 $3,960.02 $2,970.02
ple 6
89000
8
5000
325000
25000
5
530000
15000
6
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Matrix 2
X Y Z Availabale
A 15 25 30 4150B 40 30 25 5200
C 25 45 30 5950
-0.016364 0.04363636 -0.02
-0.041818 -0.0218182 0.06
0.0763636 -0.0036364 -0.04
X 40Y 70
Z 60
Matrix 2
Car Labour HourMaterials
Used
Subcontracted
WorksCost of Car
A 40 100 50 18000
B 80 150 80 28000
C 100 250 100 42000
-0.1 0.05 0.01
0 -0.02 0.016
0.1 0 -0.04
Labour
Hour20
Materials
Cost112
Example 1
Mmult
Inverse
Matrix 1
Example 2
Manufacturing Company
Matrix 1
Inverse
Mmult
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Subcon.
Cost120
Matrix 2
X Y Z
3 -5 4 11
5 2 -7 -12
1 4 3 42
0.1197183 0.10915493 0.09507
-0.077465 0.01760563 0.144366
0.0633803 -0.0598592 0.109155
X 4
Y 5
Z 6
Matrix 2
P Q R
A 1 2 1 8
B 2 3 2 14
C 3 2 2 13
2 -2 1
2 -1 0
-5 4 -1
P 1
Q 2
R 3
Inverse
Mmult
Example 4Matrix 1
Example 3
Matrix 1
Inverse
Mmult
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Matrix 2
x y z Tk.
A 2 5 3 480
B 4 3 6 750
C 1 4 10 710
-0.05042 0.31932773 -0.176471
0.2857143 -0.1428571 0
-0.109244 0.02521008 0.117647
x 90
y 30
z 50
Matrix 2
X Y Z
1 -1 1 71 2 3 16
1 3 4 22
-1 7 -5
-1 3 -2
1 -4 3
x -5y -3
z 9
Example 7
Matrix 1
Inverse
Mmult
Example 6
Matrix 1
Inverse
Mmult
Example 5
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Matrix 2
X Y Z
Day1 1 10 50 7000
Day2 1 10 40 6500
Day3 1 15 50 7500
-2 5 -2
-0.2 0 0.2
0.1 -0.1 0
X 3500
Y 100
Z 50
Matrix 2
X Y Z
5 2 -8 -28
7 -6 3 48
-2 4 4 32
0.0957447 0.10638298 0.111702
0.0904255 -0.0106383 0.18883
-0.042553 0.06382979 0.117021
x 6
y 3
z 8
Matrix 2
X Y Z
A 5 8 -3 4900
Inverse
Mmult
Matrix 1
Example 9
Matrix 1
Matrix 1
Inverse
Mmult
Example 8
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B 8 -3 6 8000
C -4 7 6 3600
0.0595238 0.06845238 -0.03869
0.0714286 -0.0178571 0.053571
-0.043651 0.06646825 0.078373
X 700
Y 400
Z 600
Matrix 2
Customer X Y Z
A 6 12 5 1680
B 5 8 14 1850
C 16 7 3 2110
-0.046279 -0.0006254 0.08005
0.1307067 -0.0387742 -0.036898-0.058161 0.09380863 -0.007505
X 90
Y 70
Z 60
Matrix 2
Mango Apple Bannana Cost
Hamid 8 10 4 1630
Jamil 7 2 5 980
Zahid 6 9 3 1335
Example 11
Matrix 1
Inverse
Mmult
Example 10
Matrix 1
Inverse
Mmult
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2.1666667 -0.3333333 -2.333333
-0.5 0 0.666667
-2.833333 0.66666667 3
Mango 90Apple 75
Bannana 40
Matrix 2
Men Women Child C. Allowances
A 2 3 1 12300
B 1 1 2 7900
C 1 2 3 11600
0.25 1.75 -1.25
0.25 -1.25 0.75
-0.25 0.25 0.25
Men 2400
Women 1900
Child 1800
Matrix 2
A B C Profit
Method 1 4 8 2 84
Method 2 5 7 1 84
Method 3 5 3 9 116
-0.5 0.55 0.05
0.3333333 -0.2166667 -0.05
Inverse
Example 13
Matrix 1
Inverse
Mmult
Example 12
Matrix 1
Inverse
Mmult
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0.1666667 -0.2333333 0.1
A 10
B 4
C 6
Matrix 2
Engineer Foreman Worker Salary
Dhaka 2 6 42 492000
Ctg 1 4 36 356000
Rajshahi 1 3 24 264000
-2 -3 8
2 1 -5
-0.166667 0 0.333333
Engineer 60000
Foreman 20000
Worker 6000
Inverse
Mmult
Example 14
Matrix 1
Mmult
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No of Flights 9
No of Employees 6
Flight Schedules 60480
Boys Girls
Total Members 6 4
selected members 4 2
calculation of combination 15 6
selected committee
4 2
3 3
2 4
15 6
20 4
15 1
no of committee
Men Women
Total Members 21 4
2 1
1 2
0 3
210 4
21 6
Example 3
90
req (ii)
selected members
calculation of combination
185
Example 1
Example 2
req (i)
Selected Members
Calculation of Combination
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1 4
No of Groups
Man Woman
Total Members 6 4
3 1
2 2
1 3
0 4
20 4
15 6
6 4
1 1
selected committee
3 1
2 2
1 3
20 4
15 6
6 4
no of committee
men women
no of members 15 12
selected members 3 2
calculation 455 66
Total Combination
req (ii)
selected members
calculation of combination
30030
Example 5
194
970
Example 4
req (i)
selected members
calculation of combination
195
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Bengali English History Management
Number of Total Books 6 2 3 5
Selection 6 2 3 5
Calculatoion of Arrangement 720 2 6 120
Total Arrangement
A B
Total Members 6 4
3 2
4 1
5 0
20 6
15 4
6 1
No of Committee
Bowlers Wicket Keeper None
4 2 10
Selection 3 1 7
Calculation 4 2 120
Total Group
3 1 7
Req (ii)
24883200
Example 8
Selection of Members
Calculation of Combinations
186
Req (i)
Example 7
960
Example 6
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4 1 6
4 2 5
3 2 6
4 2 120
1 2 210
1 1 2524 1 210
Total Group
Boys & Girls Boys
Total 8 3
Selected 8 3
Calculation of Permutation 40320 6
No. of Arrangements 241920
Example 9
Selection
Calculation
2472
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Computer
4
4
24
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Product X Product Y Hours Used Time Available
Dept1 2 6 60 60
Dept2 5 3 54 60
Dept3 3 3 42 42
Products To Be
Produced6 8
Profit Per Unit 3 5
Total
Ingredient
X1
Ingredient
X2Quintals Used Quintals Available
Dept1 1 1 400 400
Dept2 1 0 160 160
Dept3 0 1 240 120
Products To Be
Produced160 240
Cost Per Unit 6 16
Total
Sports Coat Top Coat Rain Coat Hours Used
Cutting 1 2 2 60
Sewing 1 1.5 2 60
Detailing 0.5 1 1.5 45
Profit Maximization Case
Example 1
Profit Maximization Case
Example 3
58
Example 2
Cost Minimization Case
4800
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Products To Be
Produced0 0 30
Profit Per Unit 5 8 12
Total
X1 X2 Hours Used Time Available
1 2 30 40
3 1 30 30
4 3 60 60
To Be Produced 6 12
Cost Per Unit 20 10Total
A B C Hours Used
D 1 60 50 40 4000
D 2 3 2 1 144
Products To Be
Produced 29.33 0.00 56.00
Profit Per Unit 2100 1600 1300
Total
A B Hours Used Time Available
Processing 6 3 54 54
Assembly 4 6 44 48
Packageing 5 5 50 50
Example 6
Profit Maximization Case of Toys
Example 5
Profit Maximization Case
134400
240
Example 4
Minimization Case
360
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Products To Be
Produced8 2
Profit Per Unit 30 20
Total
Operation Hours Grade A Grade B Grade X Hours Used
i 2 50 10 100
ii 2 5 3 100
iii 4 2 2 200
Products To Be
Produced50 0 0
Profit Per Unit 40 30 20
Total
A B Hours Used Time Available
Grinder 3 2 40 40
Sharper 3 1 20 30
Lathe 1 2 40 40
Products To Be
Produced0 20
Profit Per Unit 2 3
Total
Product A Product B Hours Used Time Available
Raw Materials (Kg.) 60.00 120.00 12000.00 12000.00
Machine Hours 8.00 5.00 600.00 600.00
Man Hours 3.00 4.00 418.18 500.00
2000
Example 7
Product Maximization Case
Profit Maximization Case
60
Example 9
Example 8
Profit Maximization Case
280
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Products To Be
Produced18.18 90.91
Sales Price Per Unit 30.00 40.00
Total
Corn Wheat Soyabean Used
Preparation 100 120 70 100000
Man-Days 7 10 8 8000
Acre 1 1 1 875
Products To Be
Produced250 625 0
Profit Per Unit 30 40 20
Total
A B Nutrient Used Minimum Nutrient
M1 36 6 156 108
M2 3 12 36 36
M3 20 10 100 100
Products To Be
Produced4 2
Cost Per Unit 20 40
Total
Food X Food Y Units Used Units Available
Vitamin A 6 8 100 100
Vitamin B 7 12 120 120
Example 10
Profit Maximization Case
32500
Cost Minimization Case
Example 11
Cost Minimization Case
160
Example 12
4181.82
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Products To Be
Produced15 1.25
Cost Per Unit 12 20
Total
Machine Chair Table Hours Used Time Available
M1 3 3 36 36
M2 5 2 33 50
M3 2 6 60 60
Products To BeProduced
3 9
Profit Per Unit 20 30
Total
Food 1 Food 2 Used
A 7 2 30 30
B 5 4 24 20
C 2 8 16 16
Products To Be
Produced4 1
Profit Per Unit 3 2
Total
Truck A Truck B Hours Used
Cost Minimization Case
330
Example 14
205
Example 13
Profit Maximization Case
Minimization Case
14
Example 15
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Refrigereted 20 30 900 900
Non-Refrigereted 40 30 1200 1200
Products To Be
Produced15 20
Profit Per Unit 30 40
Total
M1 M2 M3 M4
Steel 6 5 3 2
Brass 3 4 9 2Man-Weeks 1 2 1 2
Products To Be
Produced14.72 0.00 3.19 1.04
Profit Per Unit 6.00 4.00 7.00 5.00
Total
A B Hours Used Time Available
Foundry 10 6 1000 1000
Machine Shop 5 4 600 600
Products To Be
Produced40 100
Profit Per Unit 30 20
Total
Example 16
Maximization Case
115.90
3200
Example 17
Case
1250
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Time Available
80
60
50
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Time Available
4000
144
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Time Available
100
400
600
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Available
100000
8000
1000
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Hours Used Time Available
100 100
75 7520 20