53
54
55
56
A B C D E F
$290 3.33 3.33 $1,967
$310 06.67 $2,067
$330 06.67 $2,200
$350 06.67 $2,333
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34
A B C D E F G H
Grandfather Wall
Clock Clock
Unit Profit $300 $200
Hours Hours
Used Available
Assembly (David) 6 4 33 <= 40
Carving (LaDeana) 8 4 40 <= 40
Shipping (Lydia) 3 3 20 <= 20
Grandfather Wall
Clock Clock Total Profit
Production 3.33 3.33 $1,665
Total Profit Unit Profit for Wall Clocks
$1,665 $50 $100 $150 $200 $250 $300
$150 $750 $833 $1,000 $1,333 $1,667 $2,000
$200 $1,000 $1,000 $1,167 $1,333 $1,667 $2,000
Unit Profit $250 $1,250 $1,250 $1,333 $1,500 $1,667 $2,000
for Grandfather $300 $1,500 $1,500 $1,500 $1,667 $1,833 $2,000
Clocks $350 $1,750 $1,750 $1,750 $1,833 $2,000 $2,167
$400 $2,000 $2,000 $2,000 $2,000 $2,167 $2,333
$450 $2,250 $2,250 $2,250 $2,250 $2,333 $2,500
Production (Grandfather Clocks, Wall Clocks) Unit Profit for Wall Clocks
(3.33,3.33) $50 $100 $150 $200 $250 $300
$150 (5,0) (3.33,3.33) (3.33,3.33) (0,6.67) (0,6.67) (0,6.67)
$200 (5,0) (5,0) (3.33,3.33) (3.33,3.33) (0,6.67) (0,6.67)
Unit Profit $250 (5,0) (5,0) (3.33,3.33) (3.33,3.33) (0,6.67) (0,6.67)
for Grandfather $300 (5,0) (5,0) (5,0) (3.33,3.33) (3.33,3.33) (0,6.67)
Clocks $350 (5,0) (5,0) (5,0) (3.33,3.33) (3.33,3.33) (3.33,3.33)
$400 (5,0) (5,0) (5,0) (5,0) (3.33,3.33) (3.33,3.33)
$450 (5,0) (5,0) (5,0) (5,0) (3.33,3.33) (3.33,3.33)
Time Required
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2
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4
5
6
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8
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10
11
12
A B C D E F
Grandfather Wall
Clock Clock
Unit Profit $300 $200
Hours Hours
Used Available
Assembly (David) 6 4 33 <= 45
Carving (LaDeana) 8 4 40 <= 40
Shipping (Lydia) 3 3 20 <= 20
Grandfather Wall
Clock Clock Total Profit
Production 3.33 3.33 $1,667
Time Required
1
2
3
4
5
6
7
8
9
10
11
12
A B C D E F
Grandfather Wall
Clock Clock
Unit Profit $300 $200
Hours Hours
Used Available
Assembly (David) 6 4 36 <= 40
Carving (LaDeana) 8 4 45 <= 45
Shipping (Lydia) 3 3 20 <= 20
Grandfather Wall
Clock Clock Total Profit
Production 4.58 2.08 $1,792
Time Required
1
2
3
4
5
6
7
8
9
10
11
12
A B C D E F
Grandfather Wall
Clock Clock
Unit Profit $300 $200
Hours Hours
Used Available
Assembly (David) 6 4 37 <= 40
Carving (LaDeana) 8 4 40 <= 40
Shipping (Lydia) 3 3 25 <= 25
Grandfather Wall
Clock Clock Total Profit
Production 1.67 6.67 $1,833
Time Required
1
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48
A B C D E F
Grandfather Wall
Clock Clock
Unit Profit $300 $200
Hours Hours
Used Available
Assembly (David) 6 4 33 <= 40
Carving (LaDeana) 8 4 40 <= 40
Shipping (Lydia) 3 3 20 <= 20
Grandfather Wall
Clock Clock Total Profit
Production 3.33 3.33 $1,667
Assembly Hours
Available Grandfather Wall
Time Required
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$12 Production Clock 3.33 0.00 300 100 100
$C$12 Production Clock 3.33 0.00 200 100 50
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$D$6 Assembly (David) Used 33 040 1E+30 6.667
$D$7 Carving (LaDeana) Used 40 25 40 13.333 13.333
$D$8 Shipping (Lydia) Used 20 33.33 20 10 5
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2
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4
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7
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9
10
11
A B C D E F
Toys Subassemblies
Unit Profit $3.00 -$2.50
Used Available
Subassembly A 2 -1 3,000 <= 3,000
Subassembly B 1 -1 1,000 <= 1,000
Toys Subassemblies Total Profit
Production 2,000 1,000 $3,500.00
<=
2,500
Resource Usage
1
2
3
4
5
6
7
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9
10
11
A B C D E F
Toys Subassemblies
Unit Profit $3.00 -$2.50
Used Available
Subassembly A 2 -1 3,001 <= 3,001
Subassembly B 1 -1 1,000 <= 1,000
Toys Subassemblies Total Profit
Production 2,001 1,001 $3,500.50
<=
2,500
Resource Usage
1
2
3
4
5
6
7
8
9
10
11
A B C D E F
Toys Subassemblies
Unit Profit $3.00 -$2.50
Used Available
Subassembly A 2 -1 3,000 <= 3,000
Subassembly B 1 -1 1,001 <= 1,001
Toys Subassemblies Total Profit
Production 1,999 998 $3,502.00
<=
2,500
Resource Usage
1
2
3
4
5
6
7
8
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A B C D E F
Toys Subassemblies
Unit Profit $3.00 -$2.50
Used Available
Subassembly A 2 -1 3,000 <= 3,000
Subassembly B 1 -1 1,000 <= 1,000
Toys Subassemblies Total Profit
Production 2,000 1,000 $3,500.00
<=
2,500
Available Total Incremental
Subassembly A Toys Subassemblies Profit Profit
2,000 1,000 $3,500.00
3,000 2,000 1,000 $3,500.00
3,100 2,100 1,100 $3,550.00 $50.00
3,200 2,200 1,200 $3,600.00 $50.00
3,300 2,300 1,300 $3,650.00 $50.00
3,400 2,400 1,400 $3,700.00 $50.00
3,500 2,500 1,500 $3,750.00 $50.00
3,600 2,500 1,500 $3,750.00 $0.00
3,700 2,500 1,500 $3,750.00 $0.00
3,800 2,500 1,500 $3,750.00 $0.00
3,900 2,500 1,500 $3,750.00 $0.00
4,000 2,500 1,500 $3,750.00 $0.00
Resource Usage
Production
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A B C D E F
Toys Subassemblies
Unit Profit $3.00 -$2.50
Used Available
Subassembly A 2 -1 3,000 <= 3,000
Subassembly B 1 -1 1,000 <= 1,000
Toys Subassemblies Total Profit
Production 2,000 1,000 $3,500.00
<=
2,500
Available Total Incremental
Subassembly B Toys Subassemblies Profit Profit
2,000 1,000 $3,500.00
1,000 2,000 1,000 $3,500.00
1,100 1,900 800 $3,700.00 $200.00
1,200 1,800 600 $3,900.00 $200.00
1,300 1,700 400 $4,100.00 $200.00
1,400 1,600 200 $4,300.00 $200.00
1,500 1,500 0$4,500.00 $200.00
1,600 1,500 0$4,500.00 $0.00
1,700 1,500 0$4,500.00 $0.00
1,800 1,500 0$4,500.00 $0.00
1,900 1,500 0$4,500.00 $0.00
2,000 1,500 0$4,500.00 $0.00
Resource Usage
Production
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$9 Production Toys 2,000 0 3 2 0.5
$C$9 Production Subassemblies 1,000 0 -2.5 1 0.5
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$D$5 Subassembly A Used 3,000 0.5 3000 500 1000
$D$6 Subassembly B Used 1,000 21000 500 500
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9
A B C D E F
Activity 1 Activity 2
Unit Profit $2 $5
Used Available
Resource 1 1 2 10 <= 10
Resource 2 1 3 12 <= 12
Activity 1 Activity 2 Total Profit
Solution 6 2 $22.00
Resource Usage
1
2
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4
5
6
7
8
9
A B C D E F
Activity 1 Activity 2
Unit Profit $2 $5
Used Available
Resource 1 1 2 11 <= 11
Resource 2 1 3 12 <= 12
Activity 1 Activity 2 Total Profit
Solution 9 1 $23.00
Resource Usage
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2
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A B C D E F
Activity 1 Activity 2
Unit Profit $2 $5
Used Available
Resource 1 1 2 10 <= 10
Resource 2 1 3 12 <= 12
Activity 1 Activity 2 Total Profit
Solution 6 2 $22.00
Available Total Incremental
Resource 1 Activity 1 Activity 2 Profit Profit
6 2 $22.00
5 0 2.5 $12.50
6 0 3 $15.00 $2.50
7 0 3.5 $17.50 $2.50
8 0 4 $20.00 $2.50
9 3 3 $21.00 $1.00
10 6 2 $22.00 $1.00
11 9 1 $23.00 $1.00
12 12 0$24.00 $1.00
13 12 0$24.00 $0.00
14 12 0$24.00 $0.00
15 12 0$24.00 $0.00
Resource Usage
Solution
1
2
3
4
5
6
7
8
9
A B C D E F
Activity 1 Activity 2
Unit Profit $2 $5
Used Available
Resource 1 1 2 10 <= 10
Resource 2 1 3 13 <= 13
Activity 1 Activity 2 Total Profit
Solution 4 3 $23.00
Resource Usage
1
2
3
4
5
6
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A B C D E F
Activity 1 Activity 2
Unit Profit $2 $5
Used Available
Resource 1 1 2 10 <= 10
Resource 2 1 3 12 <= 12
Activity 1 Activity 2 Total Profit
Solution 6 2 $22.00
Available Total Incremental
Resource 2 Activity 1 Activity 2 Profit Profit
6 2 $22.00
6 6 0 $12.00
7 7 0 $14.00 $2.00
8 8 0 $16.00 $2.00
9 9 0 $18.00 $2.00
10 10 0$20.00 $2.00
11 8 1 $21.00 $1.00
12 6 2 $22.00 $1.00
13 4 3 $23.00 $1.00
14 2 4 $24.00 $1.00
15 0 5 $25.00 $1.00
16 0 5 $25.00 $0.00
17 0 5 $25.00 $0.00
18 0 5 $25.00 $0.00
Resource Usage
Solution
Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$9 Solution Activity 1 6 0 2 0.5 0.333
$C$9 Solution Activity 2 2 0 5 1 1
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$D$5 Resource 1 Used 10 110 2 2
$D$6 Resource 2 Used 12 112 3 2