Scribd
Upload
12 views11 pages

Practice

The document contains multiple reports generated by Microsoft Excel's Solver for optimization problems, indicating successful solutions for maximizing profit under given constraints. In the first scenario, a profit of 1400 was achieved with variables x and y both set to 200, while in subsequent scenarios, profits of 150 and 160 were achieved with different variable settings. Each report includes details on variable values, constraints, and sensitivity analysis, confirming that all constraints and optimality conditions were satisfied.

Uploaded by

cherubimsmichael
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
12 views11 pages

Practice

The document contains multiple reports generated by Microsoft Excel's Solver for optimization problems, indicating successful solutions for maximizing profit under given constraints. In the first scenario, a profit of 1400 was achieved with variables x and y both set to 200, while in subsequent scenarios, profits of 150 and 160 were achieved with different variable settings. Each report includes details on variable values, constraints, and sensitivity analysis, confirming that all constraints and optimality conditions were satisfied.

Uploaded by

cherubimsmichael
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
You are on page 1/ 11

Microsoft Excel 15.

0 Answer Report
Worksheet: [Book1]Sheet1
Report Created: 11/28/2024 4:05:05 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, Use Automatic Scaling
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative

Objective Cell (Max)


Cell Name Original Value Final Value
$D$17 profit total 0 1400

Variable Cells
Cell Name Original Value Final Value Integer
$B$10 x 0 200 Contin
$C$10 y 0 200 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$D$13 C1 used 1000 $D$13<=$F$13 Binding 0
$D$14 C2 used 400 $D$14<=$F$14 Binding 0
$D$15 C3 used 200 $D$15<=$F$15 Binding 0
Microsoft Excel 15.0 Sensitivity Report
Worksheet: [Book1]Sheet1
Report Created: 11/28/2024 4:05:05 PM

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$10 x 200 0 4 1E+030 1
$C$10 y 200 0 3 1 3

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$D$13 C1 used 1000 0 1000 1E+030 0
$D$14 C2 used 400 3 400 0 200
$D$15 C3 used 200 1 200 200 0
Microsoft Excel 15.0 Limits Report
Worksheet: [Book1]Sheet1
Report Created: 11/28/2024 4:05:05 PM

Objective
Cell Name Value
$D$17 profit total 1400

Variable Lower Objective Upper Objective


Cell Name Value Limit Result Limit Result
$B$10 x 200 0 600 200 1400
$C$10 y 200 0 800 200 1400
Maximize
Z=4x+3y

2x+3y<=1000
x+y<=400
x<=200

Inputs x y
200 200

Variables used Available


C1 2 3 1000 <= 1000
C2 1 1 400 <= 400
C3 1 0 200 <= 200
total
profit 4 3 1400
Microsoft Excel 15.0 Answer Report
Worksheet: [Book1]Sheet5
Report Created: 11/28/2024 4:17:44 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.015 Seconds.
Iterations: 2 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
$E$15 Profit total 0 150

Variable Cells
Cell Name Original Value Final Value Integer
$B$8 x 0 0 Contin
$C$8 y 0 3 Contin
$D$8 z 0 15 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$E$11 C1 Used 60 $E$11<=$G$11 Binding 0
$E$12 C2 Used 72 $E$12<=$G$12 Binding 0
$E$13 C3 Used 87 $E$13<=$G$13 Not Binding 13
Microsoft Excel 15.0 Sensitivity Report
Worksheet: [Book1]Sheet5
Report Created: 11/28/2024 4:17:44 PM

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$8 x 0 -3 5 3 1E+030
$C$8 y 3 0 10 3.3333333333 2
$D$8 z 15 0 8 2 2

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$E$11 C1 Used 60 1 60 30 6
$E$12 C2 Used 72 1.25 72 8 24
$E$13 C3 Used 87 0 100 1E+030 13
Microsoft Excel 15.0 Limits Report
Worksheet: [Book1]Sheet5
Report Created: 11/28/2024 4:17:44 PM

Objective
Cell Name Value
$E$15 Profit total 150

Variable Lower Objective Upper Objective


Cell Name Value Limit Result Limit Result
$B$8 x 0 0 150 0 150
$C$8 y 3 0 120 3 150
$D$8 z 15 0 30 15 150
Microsoft Excel 15.0 Answer Report
Worksheet: [Book1]Sheet5
Report Created: 11/28/2024 4:29:16 PM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.015 Seconds.
Iterations: 2 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
$E$15 Profit total 0 160

Variable Cells
Cell Name Original Value Final Value Integer
$B$8 x 0 0 Contin
$C$8 y 0 8 Contin
$D$8 z 0 10 Contin

Constraints
Cell Name Cell Value Formula Status Slack
$E$11 C1 Used 60 $E$11<=$G$11 Binding 0
$E$12 C2 Used 72 $E$12<=$G$12 Binding 0
$E$13 C3 Used 82 $E$13<=$G$13 Not Binding 18
Microsoft Excel 15.0 Sensitivity Report
Worksheet: [Book1]Sheet5
Report Created: 11/28/2024 4:29:16 PM

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$B$8 x 0 -3.6666666667 5 3.6666666667 1E+030
$C$8 y 8 0 10 10 2
$D$8 z 10 0 8 2 4

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$E$11 C1 Used 60 0.6666666667 60 30 24
$E$12 C2 Used 72 1.6666666667 72 12.705882353 24
$E$13 C3 Used 82 0 100 1E+030 18
Microsoft Excel 15.0 Limits Report
Worksheet: [Book1]Sheet5
Report Created: 11/28/2024 4:29:16 PM

Objective
Cell Name Value
$E$15 Profit total 160

Variable Lower Objective Upper Objective


Cell Name Value Limit Result Limit Result
$B$8 x 0 0 160 0 160
$C$8 y 8 0 80 8 160
$D$8 z 10 0 80 10 160
maximize Z=5x+10y+8z

3x+5y+2z<=60
4x+4y+4z<=72
2x+4y+5z<=100

Inputs x y z
0 8 10

Variables Used available


C1 3 5 2 60 <= 60
C2 4 4 4 72 <= 72
C3 2 4 5 82 <= 100
total
Profit 5 10 8 160

You might also like