Microsoft Excel 16.

0 Answer Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 2:13:01 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 5 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 (Max)

Cell Name Original Value Final Value
$H$1 f(x) 0 1.5

Variable Cells
Cell Name Original Value Final Value Integer
$B$3 nghiem x1 0 5.5 Contin
$C$3 nghiem x2 0 0 Contin
$D$3 nghiem x3 0 0 Contin
$E$3 nghiem x4 0 1.5 Contin
$F$3 nghiem x5 0 2.5 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$H$5 he rang buoc 4 $H$5=4 Binding 0
$H$6 -4 $H$6=-4 Binding 0
$H$7 3 $H$7<=3 Binding 0
$B$3 nghiem x1 5.5 $B$3>=0 Not Binding 5.5
$C$3 nghiem x2 0 $C$3>=0 Binding 0
$D$3 nghiem x3 0 $D$3>=0 Binding 0
$E$3 nghiem x4 1.5 $E$3>=0 Not Binding 1.5
$F$3 nghiem x5 2.5 $F$3>=0 Not Binding 2.5
NonNegative
Microsoft Excel 16.0 Answer Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 2:49:02 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0 Seconds.
Iterations: 2 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
$H$1 f(x) 31 31

Variable Cells
Cell Name Original Value Final Value Integer
$B$3 nghiem x1 5 5 Contin
$C$3 nghiem x2 0 0 Contin
$D$3 nghiem x3 3 3 Contin
$E$3 nghiem x4 0 0 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$H$5 he rang buoc 5 $H$5=5 Binding 0
$H$6 6 $H$6=6 Binding 0
$B$3 nghiem x1 5 $B$3>=0 Not Binding 5
$C$3 nghiem x2 0 $C$3>=0 Binding 0
$D$3 nghiem x3 3 $D$3>=0 Not Binding 3
$E$3 nghiem x4 0 $E$3>=0 Binding 0
NonNegative
Microsoft Excel 16.0 Sensitivity Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 2:49:02 PM

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$3 nghiem x1 5 0 5 1E+030 6
$C$3 nghiem x2 0 6 1 1E+030 6
$D$3 nghiem x3 3 0 2 2 1E+030
$E$3 nghiem x4 0 1 2 1E+030 1

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$H$5 he rang buoc 5 5 5 1E+030 5
$H$6 6 1 6 1E+030 6
Microsoft Excel 16.0 Limits Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 2:49:02 PM

Objective
Cell Name Value
$H$1 f(x) 31

Variable Lower Objective Upper Objective

Cell Name Value Limit Result Limit Result
$B$3 nghiem x1 5 5 31 5 31
$C$3 nghiem x2 0 0 31 0 31
$D$3 nghiem x3 3 3 31 3 31
$E$3 nghiem x4 0 0 31 0 31
Microsoft Excel 16.0 Answer Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 3:01:38 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 3 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 (Max)

Cell Name Original Value Final Value
$H$1 f(x) -44 29.6

Variable Cells
Cell Name Original Value Final Value Integer
$B$3 nghiem x1 5.5 0 Contin
$C$3 nghiem x2 0 4.8 Contin
$D$3 nghiem x3 0 0.4 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$H$5 he rang buoc 18 $H$5=18 Binding 0
$H$6 16 $H$6=16 Binding 0
$B$3 nghiem x1 0 $B$3>=0 Binding 0
$C$3 nghiem x2 4.8 $C$3>=0 Not Binding 4.8
$D$3 nghiem x3 0.4 $D$3>=0 Not Binding 0.4
NonNegative
Microsoft Excel 16.0 Sensitivity Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 3:01:38 PM

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$3 nghiem x1 0 -15.04 -8 15.04 1E+030
$C$3 nghiem x2 4.8 0 6 1E+030 13.428571429
$D$3 nghiem x3 0.4 0 2 1E+030 94

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$H$5 he rang buoc 18 0.72 18 3.3333333333 30
$H$6 16 1.04 16 1E+030 2.5
Microsoft Excel 16.0 Limits Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 3:01:38 PM

Objective
Cell Name Value
$H$1 f(x) 29.6

Variable Lower Objective Upper Objective

Cell Name Value Limit Result Limit Result
$B$3 nghiem x1 0 -8.881784E-16 29.6 -8.881784E-16 29.6
$C$3 nghiem x2 4.8 4.8 29.6 4.8 29.6
$D$3 nghiem x3 0.4 0.4 29.6 0.4 29.6
Microsoft Excel 16.0 Answer Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 3:03:22 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.016 Seconds.
Iterations: 2 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
$H$1 f(x) 29.6 -8

Variable Cells
Cell Name Original Value Final Value Integer
$B$3 nghiem x1 0 2.5 Contin
$C$3 nghiem x2 4.8 2 Contin
$D$3 nghiem x3 0.4 0 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$H$5 he rang buoc 18 $H$5=18 Binding 0
$H$6 16 $H$6=16 Binding 0
$B$3 nghiem x1 2.5 $B$3>=0 Not Binding 2.5
$C$3 nghiem x2 2 $C$3>=0 Not Binding 2
$D$3 nghiem x3 0 $D$3>=0 Binding 0
NonNegative
Microsoft Excel 16.0 Sensitivity Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 3:03:23 PM

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$3 nghiem x1 2.5 0 -8 15.04 1E+030
$C$3 nghiem x2 2 0 6 1E+030 13.428571429
$D$3 nghiem x3 0 94 2 1E+030 94

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$H$5 he rang buoc 18 12 18 3.3333333333 2
$H$6 16 -14 16 2 2.5
Microsoft Excel 16.0 Limits Report
Worksheet: [Book1]Sheet1
Report Created: 10/30/2024 3:03:23 PM

Objective
Cell Name Value
$H$1 f(x) -8

Variable Lower Objective Upper Objective

Cell Name Value Limit Result Limit Result
$B$3 nghiem x1 2.5 2.5 -8 2.5 -8
$C$3 nghiem x2 2 2 -8 2 -8
$D$3 nghiem x3 0 0 -8 0 -8
he so ham muc tieu -8 6 2 f(x) -8
ham muc tieu x1 x2 x3
nghiem 2.5 2 0

he rang buoc 4 4 -3 18 =
4 3 4 16 =
18
16