1 2 3 4 5 6 Demand

A 9 22 58 11 19 27 1
B 43 78 72 50 63 48 1
C 41 28 91 37 45 33 1
D 74 42 27 49 39 32 1
E 36 11 57 22 25 18 1
F 3 56 53 31 17 28 1
R=C
Requireme 1 1 1 1 1 1

1 2 3 4 5 6 Demand
A 0 0 0 1 0 0 1 1
B 0 0 0 0 0 1 1 1
C 0 1 0 0 0 0 1 1
D 0 0 1 0 0 0 1 1
E 0 0 0 0 1 0 1 1
F 1 0 0 0 0 0 1 1
1 1 1 1 1 1
Requireme 1 1 1 1 1 1 1 1

Assngt Cos 142

Microsoft Excel 14.0 Answer Report
Worksheet: [LAB2.xlsx]Example
Report Created: 3/2/2024 8:23:19 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.015 Seconds.
Iterations: 27 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value
$B$23 Assngt Cost 0 142

Variable Cells
Cell Name Original Value Final Value Integer
$B$13 A 0 0 Contin
$C$13 A 0 0 Contin
$D$13 A 0 0 Contin
$E$13 A 0 1 Contin
$F$13 A 0 0 Contin
$G$13 A 0 0 Contin
$B$14 B 0 0 Contin
$C$14 B 0 0 Contin
$D$14 B 0 0 Contin
$E$14 B 0 0 Contin
$F$14 B 0 0 Contin
$G$14 B 0 1 Contin
$B$15 C 0 0 Contin
$C$15 C 0 1 Contin
$D$15 C 0 0 Contin
$E$15 C 0 0 Contin
$F$15 C 0 0 Contin
$G$15 C 0 0 Contin
$B$16 D 0 0 Contin
$C$16 D 0 0 Contin
$D$16 D 0 1 Contin
$E$16 D 0 0 Contin
$F$16 D 0 0 Contin
$G$16 D 0 0 Contin
$B$17 E 0 0 Contin
 $C$17 E 0 0 Contin
$D$17 E 0 0 Contin
$E$17 E 0 0 Contin
$F$17 E 0 1 Contin
$G$17 E 0 0 Contin
$B$18 F 0 1 Contin
$C$18 F 0 0 Contin
$D$18 F 0 0 Contin
$E$18 F 0 0 Contin
$F$18 F 0 0 Contin
$G$18 F 0 0 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$19 1 $B$19=$B$20 Binding 0
$C$19 1 $C$19=$C$20 Binding 0
$D$19 1 $D$19=$D$20 Binding 0
$E$19 1 $E$19=$E$20 Binding 0
$F$19 1 $F$19=$F$20 Binding 0
$G$19 1 $G$19=$G$20 Binding 0
$H$13 A R = C 1 $H$13>=$I$13 Binding 0
$H$14 B R = C 1 $H$14>=$I$14 Binding 0
$H$15 C R = C 1 $H$15>=$I$15 Binding 0
$H$16 D R = C 1 $H$16>=$I$16 Binding 0
$H$17 E R = C 1 $H$17>=$I$17 Binding 0
$H$18 F R = C 1 $H$18>=$I$18 Binding 0
 1 2 3 4
1 15 13 14 17
2 11 12 15 13
3 13 12 10 11
4 15 17 14 16
R=C

1 2 3 4 Demand
1 0 1 0 0 1 1
2 1 0 0 0 1 1
3 0 0 0 1 1 1
4 0 0 1 0 1 1
1 1 1 1
Requireme 1 1 1 1

49
Microsoft Excel 14.0 Answer Report
Worksheet: [LAB2.xlsx]Sum1
Report Created: 3/2/2024 8:28:29 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 15 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value
$B$18 0 49

Variable Cells
Cell Name Original Value Final Value Integer
$B$11 0 0 Contin
$C$11 0 1 Contin
$D$11 0 0 Contin
$E$11 0 0 Contin
$B$12 0 1 Contin
$C$12 0 0 Contin
$D$12 0 0 Contin
$E$12 0 0 Contin
$B$13 0 0 Contin
$C$13 0 0 Contin
$D$13 0 0 Contin
$E$13 0 1 Contin
$B$14 0 0 Contin
$C$14 0 0 Contin
$D$14 0 1 Contin
$E$14 0 0 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$15 1 $B$15=$B$16 Binding 0
$C$15 1 $C$15=$C$16 Binding 0
$D$15 1 $D$15=$D$16 Binding 0
$E$15 1 $E$15=$E$16 Binding 0
$F$11 1 $F$11>=$G$11 Binding 0
$F$12 1 $F$12>=$G$12 Binding 0
$F$13 1 $F$13>=$G$13 Binding 0
$F$14 1 $F$14>=$G$14 Binding 0
 M1 M2 M3 M4
J1 5 7 11 6
J2 8 5 9 6
J3 4 7 10 7
J4 10 4 8 3
R=C

M1 M2 M3 M4 Demand
J1 0 1 0 0 1 1
J2 0 0 1 0 1 1
J3 1 0 0 0 1 1
J4 0 0 0 1 1 1
1 1 1 1
Req 1 1 1 1

23
Microsoft Excel 14.0 Answer Report
Worksheet: [LAB2.xlsx]Sum 2
Report Created: 3/2/2024 8:37:17 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0 Seconds.
Iterations: 10 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value
$B$14 M1 0 1

Variable Cells
Cell Name Original Value Final Value Integer
$B$10 J1 M1 0 0 Contin
$C$10 J1 M2 0 1 Contin
$D$10 J1 M3 0 0 Contin
$E$10 J1 M4 0 0 Contin
$B$11 J2 M1 0 0 Contin
$C$11 J2 M2 0 0 Contin
$D$11 J2 M3 0 1 Contin
$E$11 J2 M4 0 0 Contin
$B$12 J3 M1 0 1 Contin
$C$12 J3 M2 0 0 Contin
$D$12 J3 M3 0 0 Contin
$E$12 J3 M4 0 0 Contin
$B$13 J4 M1 0 0 Contin
$C$13 J4 M2 0 0 Contin
$D$13 J4 M3 0 0 Contin
$E$13 J4 M4 0 1 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$14 M1 1 $B$14=$B$15 Binding 0
$C$14 M2 1 $C$14=$C$15 Binding 0
$D$14 M3 1 $D$14=$D$15 Binding 0
$E$14 M4 1 $E$14=$E$15 Binding 0
$F$10 J1 1 $F$10>=$G$10 Binding 0
$F$11 J2 1 $F$11>=$G$11 Binding 0
$F$12 J3 1 $F$12>=$G$12 Binding 0
$F$13 J4 1 $F$13>=$G$13 Binding 0
 I II III IV V
1 11 17 8 16 20
2 9 7 12 6 15
3 13 16 15 12 16
4 21 24 17 28 26
5 14 10 12 11 13
R=C

I II III IV V Demand
1 1 0 0 0 0 1 1
2 0 1 0 0 0 1 1
3 0 0 0 1 0 1 1
4 0 0 1 0 0 1 1
5 0 0 0 0 1 1 1
1 1 1 1 1
Req 1 1 1 1 1

60
Microsoft Excel 14.0 Answer Report
Worksheet: [LAB2.xlsx]Sum 3
Report Created: 3/2/2024 8:41:25 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 19 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value
$B$19 I 0 60

Variable Cells
Cell Name Original Value Final Value Integer
$B$11 I 0 1 Contin
$C$11 II 0 0 Contin
$D$11 III 0 0 Contin
$E$11 IV 0 0 Contin
$F$11 V 0 0 Contin
$B$12 I 0 0 Contin
$C$12 II 0 1 Contin
$D$12 III 0 0 Contin
$E$12 IV 0 0 Contin
$F$12 V 0 0 Contin
$B$13 I 0 0 Contin
$C$13 II 0 0 Contin
$D$13 III 0 0 Contin
$E$13 IV 0 1 Contin
$F$13 V 0 0 Contin
$B$14 I 0 0 Contin
$C$14 II 0 0 Contin
$D$14 III 0 1 Contin
$E$14 IV 0 0 Contin
$F$14 V 0 0 Contin
$B$15 I 0 0 Contin
$C$15 II 0 0 Contin
$D$15 III 0 0 Contin
$E$15 IV 0 0 Contin
$F$15 V 0 1 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$B$16 I 1 $B$16=$B$17 Binding 0
$C$16 II 1 $C$16=$C$17 Binding 0
$D$16 III 1 $D$16=$D$17 Binding 0
$E$16 IV 1 $E$16=$E$17 Binding 0
$F$16 V 1 $F$16=$F$17 Binding 0
$G$11 1 $G$11>=$H$11 Binding 0
$G$12 1 $G$12>=$H$12 Binding 0
$G$13 1 $G$13>=$H$13 Binding 0
$G$14 1 $G$14>=$H$14 Binding 0
$G$15 1 $G$15>=$H$15 Binding 0
 1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 14 10 13 13 12
E 8 12 11 7 13 10
R != C

1 2 3 4 5 6
A 0 0 0 0 0 0 0 1
B 0 0 0 0 0 0 0 1
C 0 0 0 0 0 0 0 1
D 0 0 0 0 0 0 0 1
E 0 0 0 0 0 0 0 1

0 0 0 0 0 0
1 1 1 1 1 1

0
 1 2 3 4 5 6
A 12 10 15 22 18 8
B 10 18 25 15 16 12
C 11 10 3 8 5 9
D 6 14 10 13 13 12
E 8 12 11 7 13 10
F 0 0 0 0 0 0

1 2 3 4 5 6
A 0 1 0 0 0 0
B 0 0 0 0 0 1
C 0 0 1 0 0 0
D 1 0 0 0 0 0
E 0 0 0 1 0 0
F 0 0 0 0 1 0
1 1 1 1 1 1
1 1 1 1 1 1

38
1 1
1 1
1 1
1 1
1 1
1 1
Microsoft Excel 14.0 Answer Report
Worksheet: [LAB2.xlsx]Sum 4
Report Created: 3/2/2024 9:00:44 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.015 Seconds.
Iterations: 31 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value
$N$22 0 38

Variable Cells
Cell Name Original Value Final Value Integer
$N$13 A 0 0 Contin
$O$13 A 0 1 Contin
$P$13 A 0 0 Contin
$Q$13 A 0 0 Contin
$R$13 A 0 0 Contin
$S$13 A 0 0 Contin
$N$14 B 0 0 Contin
$O$14 B 0 0 Contin
$P$14 B 0 0 Contin
$Q$14 B 0 0 Contin
$R$14 B 0 0 Contin
$S$14 B 0 1 Contin
$N$15 C 0 0 Contin
$O$15 C 0 0 Contin
$P$15 C 0 1 Contin
$Q$15 C 0 0 Contin
$R$15 C 0 0 Contin
$S$15 C 0 0 Contin
$N$16 D 0 1 Contin
$O$16 D 0 0 Contin
$P$16 D 0 0 Contin
$Q$16 D 0 0 Contin
$R$16 D 0 0 Contin
$S$16 D 0 0 Contin
$N$17 E 0 0 Contin
 $O$17 E 0 0 Contin
$P$17 E 0 0 Contin
$Q$17 E 0 1 Contin
$R$17 E 0 0 Contin
$S$17 E 0 0 Contin
$N$18 F 0 0 Contin
$O$18 F 0 0 Contin
$P$18 F 0 0 Contin
$Q$18 F 0 0 Contin
$R$18 F 0 1 Contin
$S$18 F 0 0 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$N$19 1 $N$19=$N$20 Binding 0
$O$19 1 $O$19=$O$20 Binding 0
$P$19 1 $P$19=$P$20 Binding 0
$Q$19 1 $Q$19=$Q$20 Binding 0
$R$19 1 $R$19=$R$20 Binding 0
$S$19 1 $S$19=$S$20 Binding 0
$U$13 A 1 $U$13>=$V$13 Binding 0
$U$14 B 1 $U$14>=$V$14 Binding 0
$U$15 C 1 $U$15>=$V$15 Binding 0
$U$16 D 1 $U$16>=$V$16 Binding 0
$U$17 E 1 $U$17>=$V$17 Binding 0
$U$18 F 1 $U$18>=$V$18 Binding 0
 1 2 3 4
A 16 10 14 11
B 14 11 15 15
C 15 15 13 12
D 13 12 14 15
R=C

1 2 3 4 Demand
A 1 0 0 0 1 1
B 0 0 1 0 1 1
C 0 1 0 0 1 1
D 0 0 0 1 1 1
1 1 1 1
Req 1 1 1 1

61
Microsoft Excel 14.0 Answer Report
Worksheet: [LAB2.xlsx]Sum 6
Report Created: 3/2/2024 8:48:40 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0 Seconds.
Iterations: 13 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Max)

Cell Name Original Value Final Value
$B$18 0 61

Variable Cells
Cell Name Original Value Final Value Integer
$B$11 A 0 1 Contin
$C$11 A 0 0 Contin
$D$11 A 0 0 Contin
$E$11 A 0 0 Contin
$B$12 B 0 0 Contin
$C$12 B 0 0 Contin
$D$12 B 0 1 Contin
$E$12 B 0 0 Contin
$B$13 C 0 0 Contin
$C$13 C 0 1 Contin
$D$13 C 0 0 Contin
$E$13 C 0 0 Contin
$B$14 D 0 0 Contin
$C$14 D 0 0 Contin
$D$14 D 0 0 Contin
$E$14 D 0 1 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$15 1 $B$15=$B$16 Binding 0
$C$15 1 $C$15=$C$16 Binding 0
$D$15 1 $D$15=$D$16 Binding 0
$E$15 1 $E$15=$E$16 Binding 0
$F$11 A 1 $F$11>=$G$11 Binding 0
$F$12 B 1 $F$12>=$G$12 Binding 0
$F$13 C 1 $F$13>=$G$13 Binding 0
$F$14 D 1 $F$14>=$G$14 Binding 0
 1 2 3 4 5
1 10 12 15 12 8
2 7 16 14 14 11
3 13 14 7 9 9
4 12 10 11 13 10
5 8 13 15 11 15
R=C

1 2 3 4 5
1 0 0 0 0 1 1 1
2 1 0 0 0 0 1 1
3 0 0 1 0 0 1 1
4 0 1 0 0 0 1 1
5 0 0 0 1 0 1 1
1 1 1 1 1
1 1 1 1 1

43
Microsoft Excel 14.0 Answer Report
Worksheet: [LAB2.xlsx]Q1 - GCR
Report Created: 3/2/2024 9:13:21 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0 Seconds.
Iterations: 21 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value
$B$21 0 43

Variable Cells
Cell Name Original Value Final Value Integer
$B$13 0 0 Contin
$C$13 0 0 Contin
$D$13 0 0 Contin
$E$13 0 0 Contin
$F$13 0 1 Contin
$B$14 0 1 Contin
$C$14 0 0 Contin
$D$14 0 0 Contin
$E$14 0 0 Contin
$F$14 0 0 Contin
$B$15 0 0 Contin
$C$15 0 0 Contin
$D$15 0 1 Contin
$E$15 0 0 Contin
$F$15 0 0 Contin
$B$16 0 0 Contin
$C$16 0 1 Contin
$D$16 0 0 Contin
$E$16 0 0 Contin
$F$16 0 0 Contin
$B$17 0 0 Contin
$C$17 0 0 Contin
$D$17 0 0 Contin
$E$17 0 1 Contin
$F$17 0 0 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$B$18 1 $B$18=$B$19 Binding 0
$C$18 1 $C$18=$C$19 Binding 0
$D$18 1 $D$18=$D$19 Binding 0
$E$18 1 $E$18=$E$19 Binding 0
$F$18 1 $F$18=$F$19 Binding 0
$G$13 1 $G$13>=$H$13 Binding 0
$G$14 1 $G$14>=$H$14 Binding 0
$G$15 1 $G$15>=$H$15 Binding 0
$G$16 1 $G$16>=$H$16 Binding 0
$G$17 1 $G$17>=$H$17 Binding 0
 1 2 3 4 5
1 30 39 31 38 40
2 43 37 32 35 38
3 34 41 33 41 34
4 39 36 43 32 36
5 32 49 35 40 37
6 36 42 35 44 42 R != C

1 2 3 4 5 6
1 30 39 31 38 40 0
2 43 37 32 35 38 0
3 34 41 33 41 34 0
4 39 36 43 32 36 0
5 32 49 35 40 37 0
6 36 42 35 44 42 0

1 2 3 4 5 6
1 0 0 1 0 0 0 1 1
2 0 1 0 0 0 0 1 1
3 0 0 0 0 1 0 1 1
4 0 0 0 1 0 0 1 1
5 1 0 0 0 0 0 1 1
6 0 0 0 0 0 1 1 1
1 1 1 1 1 1
1 1 1 1 1 1
166
Microsoft Excel 14.0 Answer Report
Worksheet: [LAB2.xlsx]Q2 - GCR
Report Created: 3/2/2024 9:18:00 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 27 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Min)

Cell Name Original Value Final Value
$B$27 0 166

Variable Cells
Cell Name Original Value Final Value Integer
$B$19 0 0 Contin
$C$19 0 0 Contin
$D$19 0 1 Contin
$E$19 0 0 Contin
$F$19 0 0 Contin
$G$19 0 0 Contin
$B$20 0 0 Contin
$C$20 0 1 Contin
$D$20 0 0 Contin
$E$20 0 0 Contin
$F$20 0 0 Contin
$G$20 0 0 Contin
$B$21 0 0 Contin
$C$21 0 0 Contin
$D$21 0 0 Contin
$E$21 0 0 Contin
$F$21 0 1 Contin
$G$21 0 0 Contin
$B$22 0 0 Contin
$C$22 0 0 Contin
$D$22 0 0 Contin
$E$22 0 1 Contin
$F$22 0 0 Contin
$G$22 0 0 Contin
$B$23 0 1 Contin
 $C$23 0 0 Contin
$D$23 0 0 Contin
$E$23 0 0 Contin
$F$23 0 0 Contin
$G$23 0 0 Contin
$B$24 0 0 Contin
$C$24 0 0 Contin
$D$24 0 0 Contin
$E$24 0 0 Contin
$F$24 0 0 Contin
$G$24 0 1 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$B$25 1 $B$25=$B$26 Binding 0
$C$25 1 $C$25=$C$26 Binding 0
$D$25 1 $D$25=$D$26 Binding 0
$E$25 1 $E$25=$E$26 Binding 0
$F$25 1 $F$25=$F$26 Binding 0
$G$25 1 $G$25=$G$26 Binding 0
$H$19 1 $H$19>=$I$19 Binding 0
$H$20 1 $H$20>=$I$20 Binding 0
$H$21 1 $H$21>=$I$21 Binding 0
$H$22 1 $H$22>=$I$22 Binding 0
$H$23 1 $H$23>=$I$23 Binding 0
$H$24 1 $H$24>=$I$24 Binding 0