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    LP - Ommd

    Uploaded by

    o3283
    The document contains several Solver reports from Microsoft Excel that optimized objectives subject to constraints for different worksheets. The first report optimized profits from table and chair production given constraints on carpentry and painting. It found a solution with 30 tables and 40 chairs producing $410 profit. The second report optimized production levels of three products given constraints on labor, machines, and materials. It found a solution with 48 units of Product 1, 0 of Product 2, and 28 of Product 3 for $588 total. The third report optimized an objective cell given constraints, initially finding a solution with a variable set to 50. It was rerun multiple times with different solvers and additional variables, always satisfying all constraints.

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    © All Rights Reserved
    Download as XLSX, PDF, TXT or read online from Scribd

    LP - Ommd

    Uploaded by

    o3283
    34 views16 pages
    The document contains several Solver reports from Microsoft Excel that optimized objectives subject to constraints for different worksheets. The first report optimized profits from table and chair production given constraints on carpentry and painting. It found a solution with 30 tables and 40 chairs producing $410 profit. The second report optimized production levels of three products given constraints on labor, machines, and materials. It found a solution with 48 units of Product 1, 0 of Product 2, and 28 of Product 3 for $588 total. The third report optimized an objective cell given constraints, initially finding a solution with a variable set to 50. It was rerun multiple times with different solvers and additional variables, always satisfying all constraints.

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    LP formulation

    Original Title

    LP- OMMD

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    The document contains several Solver reports from Microsoft Excel that optimized objectives subject to constraints for different worksheets. The first report optimized profits from table and chair production given constraints on carpentry and painting. It found a solution with 30 tables and 40 chairs producing $410 profit. The second report optimized production levels of three products given constraints on labor, machines, and materials. It found a solution with 48 units of Product 1, 0 of Product 2, and 28 of Product 3 for $588 total. The third report optimized an objective cell given constraints, initially finding a solution with a variable set to 50. It was rerun multiple times with different solvers and additional variables, always satisfying all constraints.

    Copyright:

    © All Rights Reserved
    Download as XLSX, PDF, TXT or read online from Scribd
    Download as xlsx, pdf, or txt
    34 views16 pages

    LP - Ommd

    Uploaded by

    o3283
    The document contains several Solver reports from Microsoft Excel that optimized objectives subject to constraints for different worksheets. The first report optimized profits from table and chair production given constraints on carpentry and painting. It found a solution with 30 tables and 40 chairs producing $410 profit. The second report optimized production levels of three products given constraints on labor, machines, and materials. It found a solution with 48 units of Product 1, 0 of Product 2, and 28 of Product 3 for $588 total. The third report optimized an objective cell given constraints, initially finding a solution with a variable set to 50. It was rerun multiple times with different solvers and additional variables, always satisfying all constraints.

    Copyright:

    © All Rights Reserved
    Download as XLSX, PDF, TXT or read online from Scribd
    Download as xlsx, pdf, or txt
    of 16

    Microsoft Excel 14.

    0 Answer Report
    Worksheet: [OMMD.xlsx]Sheet1
    Report Created: 29-Aug-2014 11:53:14 AM
    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, 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$3 Profit 410 410
    Variable Cells
    Cell Name Original Value Final Value Integer
    $B$4 Table 30 30 Contin
    $C$4 Chair 40 40 Contin
    Constraints
    Cell Name Cell Value Formula Status Slack
    $E$8 Carpentry 240 $E$8<=$G$8 Binding 0
    $E$9 Paint 100 $E$9<=$G$9 Binding 0
    Microsoft Excel 14.0 Sensitivity Report
    Worksheet: [OMMD.xlsx]Sheet1
    Report Created: 29-Aug-2014 11:53:14 AM
    Variable Cells
    Final Reduced Objective Allowable Allowable
    Cell Name Value Cost Coefficient Increase Decrease
    $B$4 Table 30 0 7 3 0.333333333
    $C$4 Chair 40 0 5 0.25 1.5
    Constraints
    Final Shadow Constraint Allowable Allowable
    Cell Name Value Price R.H. Side Increase Decrease
    $E$8 Carpentry 240 1.5 240 60 40
    $E$9 Paint 100 0.5 100 20 20
    Table Chair
    Profit 7 5 410
    30 40
    Carpentry 4 3 240 240
    Paint 2 1 100 100
    Microsoft Excel 14.0 Answer Report
    Worksheet: [OMMD.xlsx]Sheet2
    Report Created: 29-Aug-2014 12:00:03 PM
    Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
    Solver Engine
    Engine: Simplex LP
    Solution Time: 0 Seconds.
    Iterations: 3 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
    $F$2 0 588
    Variable Cells
    Cell Name Original Value Final Value Integer
    $B$3 Prod 1 0 48 Contin
    $C$3 Prod 2 0 0 Contin
    $D$3 Prod 3 0 28 Contin
    Constraints
    Cell Name Cell Value Formula Status Slack
    $F$7 Labour 360 $F$7<=$G$7 Binding 0
    $F$8 Machine 264 $F$8<=$G$8 Not Binding 36
    $F$9 Material 600 $F$9<=$G$9 Binding 0
    Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative
    Microsoft Excel 14.0 Sensitivity Report
    Worksheet: [OMMD.xlsx]Sheet2
    Report Created: 29-Aug-2014 12:00:03 PM
    Variable Cells
    Final Reduced Objective Allowable Allowable
    Cell Name Value Cost Coefficient Increase Decrease
    $B$3 Prod 1 48 0 7 6.5 1
    $C$3 Prod 2 0 -4.5 3 4.5 1E+30
    $D$3 Prod 3 28 0 9 1.5 4.333333333
    Constraints
    Final Shadow Constraint Allowable Allowable
    Cell Name Value Price R.H. Side Increase Decrease
    $F$7 Labour 360 1.3 360 25.71428571 93.33333333
    $F$8 Machine 264 0 300 1E+30 36
    $F$9 Material 600 0.2 600 210 90
    Prod 1 Prod 2 Prod 3
    7 3 9 588
    48 0 28
    Labour 4 5 6 360 360
    Machine 2 4 6 264 300
    Material 9 5 6 600 600
    Microsoft Excel 14.0 Answer Report
    Worksheet: [OMMD.xlsx]Sheet3
    Report Created: 06-Sep-2014 8:16:52 PM
    Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
    Solver Engine
    Engine: GRG Nonlinear
    Solution Time: 0 Seconds.
    Iterations: 2 Subproblems: 0
    Solver Options
    Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
    Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
    Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative
    Objective Cell (Max)
    Cell Name Original Value Final Value
    $F$2 0 500
    Variable Cells
    Cell Name Original Value Final Value Integer
    $C$3 0 50 Contin
    Constraints
    Cell Name Cell Value Formula Status Slack
    $E$7 200 $E$7<=$F$7 Not Binding 40
    $E$8 100 $E$8<=$F$8 Binding 0
    Microsoft Excel 14.0 Sensitivity Report
    Worksheet: [OMMD.xlsx]Sheet3
    Report Created: 06-Sep-2014 8:16:52 PM
    Variable Cells
    Final Reduced
    Cell Name Value Gradient
    $C$3 50 0
    Constraints
    Final Lagrange
    Cell Name Value Multiplier
    $E$7 200 0
    $E$8 100 5
    Microsoft Excel 14.0 Answer Report
    Worksheet: [OMMD.xlsx]Sheet3
    Report Created: 06-Sep-2014 8:17:42 PM
    Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
    Solver Engine
    Engine: GRG Nonlinear
    Solution Time: 0 Seconds.
    Iterations: 0 Subproblems: 0
    Solver Options
    Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling
    Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Forward, Require Bounds
    Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative
    Objective Cell (Max)
    Cell Name Original Value Final Value
    $F$2 500 500
    Variable Cells
    Cell Name Original Value Final Value Integer
    $C$3 50 50 Contin
    $D$3 0 0 Contin
    Constraints
    Cell Name Cell Value Formula Status Slack
    $E$7 200 $E$7<=$F$7 Not Binding 40
    $E$8 100 $E$8<=$F$8 Binding 0
    Microsoft Excel 14.0 Sensitivity Report
    Worksheet: [OMMD.xlsx]Sheet3
    Report Created: 06-Sep-2014 8:17:43 PM
    Variable Cells
    Final Reduced
    Cell Name Value Gradient
    $C$3 50 0
    $D$3 0 0
    Constraints
    Final Lagrange
    Cell Name Value Multiplier
    $E$7 200 0
    $E$8 100 5
    Microsoft Excel 14.0 Answer Report
    Worksheet: [OMMD.xlsx]Sheet3
    Report Created: 06-Sep-2014 8:19:22 PM
    Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
    Solver Engine
    Engine: Simplex LP
    Solution Time: 0.015 Seconds.
    Iterations: 1 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
    $F$2 0 500
    Variable Cells
    Cell Name Original Value Final Value Integer
    $C$3 0 50 Contin
    $D$3 0 0 Contin
    Constraints
    Cell Name Cell Value Formula Status Slack
    $E$7 200 $E$7<=$F$7 Not Binding 40
    $E$8 100 $E$8<=$F$8 Binding 0
    Microsoft Excel 14.0 Sensitivity Report
    Worksheet: [OMMD.xlsx]Sheet3
    Report Created: 06-Sep-2014 8:19:22 PM
    Variable Cells
    Final Reduced Objective Allowable Allowable
    Cell Name Value Cost Coefficient Increase Decrease
    $C$3 50 0 10 1E+30 0
    $D$3 0 0 5 0 1E+30
    Constraints
    Final Shadow Constraint Allowable Allowable
    Cell Name Value Price R.H. Side Increase Decrease
    $E$7 200 0 240 1E+30 40
    $E$8 100 5 100 20 100
    Microsoft Excel 14.0 Answer Report
    Worksheet: [OMMD.xlsx]Sheet3
    Report Created: 06-Sep-2014 8:32:44 PM
    Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
    Solver Engine
    Engine: Simplex LP
    Solution Time: 0 Seconds.
    Iterations: 1 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$3 0 80
    Variable Cells
    Cell Name Original Value Final Value Integer
    $C$3 0 0 Contin
    $D$3 0 80 Contin
    Constraints
    Cell Name Cell Value Formula Status Slack
    $E$7 240 $E$7<=$F$7 Binding 0
    $E$8 80 $E$8<=$F$8 Not Binding 20
    $E$9 400 $E$9<=$F$9 Not Binding 100
    Microsoft Excel 14.0 Sensitivity Report
    Worksheet: [OMMD.xlsx]Sheet3
    Report Created: 06-Sep-2014 8:32:44 PM
    Variable Cells
    Final Reduced Objective Allowable Allowable
    Cell Name Value Cost Coefficient Increase Decrease
    $C$3 0 -1.333333333 0 1.333333333 1E+30
    $D$3 80 0 1 1E+30 1
    Constraints
    Final Shadow Constraint Allowable Allowable
    Cell Name Value Price R.H. Side Increase Decrease
    $E$7 240 0.333333333 240 60 240
    $E$8 80 0 100 1E+30 20
    $E$9 400 0 500 1E+30 100
    10 5 500
    30 40
    4 3 240 240
    2 1 100 100
    10 5 500 500

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