University of Business and Technology College of Engineering Industrial Engineering Department Spring 2018 IE 311 Operations Research Contest Problems The following problems are for extra marks. They...

Answer Report 1
    Microsoft Excel 15.0 Answer Report
    Worksheet: [30374.xlsx]Sheet1
    Report Created: 07/05/2018 22:38:20
    Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
    Solver Engine
        Engine: Simplex LP
        Solution Time: 0.187 Seconds.
        Iterations: 28 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
        $D$2    P1 min total manufacturing cost    4406.25    66293.75
    Variable Cells
        Cell    Name    Original Value    Final Value    Integer
        $B$2    P1    0    360    Contin
        $B$3    P2    0    20    Contin
        $B$4    P3    0    400    Contin
        $B$5    P4    0    380    Contin
        $B$6    P5    0    50    Contin
        $B$7    P6    0    300    Contin
        $B$8    P7    0    250    Contin
        $B$9    P8    0    400    Contin
        $B$10    P9    0    20    Contin
        $B$11    P10    0    400    Contin
        $B$12    P11    0    380    Contin
        $B$13    P12    50    50    Contin
        $B$14    B1    0    90    Contin
        $B$15    B2    0    350    Contin
        $B$16    B3    0    70    Contin
        $B$17    B4    0    270    Contin
        $B$18    B5    0    350    Contin
        $B$19    B6    0    0    Contin
        $B$20    B7    0    0    Contin
        $B$21    B8    0    50    Contin
        $B$22    B9    0    350    Contin
        $B$23    B10    850    70    Contin
        $B$24    B11    650    270    Contin
        $B$25    B12    350    350    Contin
        $B$26    B13    0    0    Contin
    Constraints
        Cell    Name    Cell Value    Formula    Status    Slack
        $D$6    month 1 production levels    360    $D$6<=$F$6    Not Binding    40
        $D$7    month 2 production levels    20    $D$7<=$F$7    Not Binding    330
        $D$8    month 3 production levels    400    $D$8<=$F$8    Binding    0
        $D$9    month 4 production levels    380    $D$9<=$F$9    Binding    0
        $D$10    month 5 production levels    50    $D$10<=$F$10    Not Binding    350
        $D$11    month 6 production levels    300    $D$11<=$F$11    Binding    0
        $D$12    month 7 production levels    250    $D$12<=$F$12    Not Binding    50
        $D$13    month 8 production levels    400    $D$13<=$F$13    Binding    0
        $D$14    month 9 production levels    20    $D$14<=$F$14    Not Binding    330
        $D$15    month 10 production levels    400    $D$15<=$F$15    Binding    0
        $D$16    month 11 production levels    380    $D$16<=$F$16    Binding    0
        $D$17    month 12 production levels    50    $D$17<=$F$17    Not Binding    350
        $H$6    LE ending inventory    350    $H$6<=$J$6    Binding    0
        $H$7    LE ending inventory    70    $H$7<=$J$7    Not Binding    280
        $H$8    LE ending inventory    270    $H$8<=$J$8    Not Binding    80
        $H$9    LE ending inventory    350    $H$9<=$J$9    Binding    0
        $H$10    LE ending inventory    0    $H$10<=$J$10    Not Binding    350
        $H$11    LE ending inventory    0    $H$11<=$J$11    Not Binding    350
        $H$12    LE ending inventory    50    $H$12<=$J$12    Not Binding    300
        $H$13    LE ending inventory    350    $H$13<=$J$13    Binding    0
        $H$14    LE ending inventory    70    $H$14<=$J$14    Not Binding    280
        $H$15    LE ending inventory    270    $H$15<=$J$15    Not Binding    80
        $H$16    LE ending inventory    350    $H$16<=$J$16    Binding    0
        $H$17    LE ending inventory    0    $H$17<=$J$17    Not Binding    350
        $L$6    LE Beginning balances    90    $L$6=$N$6    Binding    0
        $L$7    LE Beginning balances    100    $L$7=$N$7    Binding    0
        $L$8    LE Beginning balances    300    $L$8=$N$8    Binding    0
        $L$9    LE Beginning balances    200    $L$9=$N$9    Binding    0
        $L$10    LE Beginning balances    300    $L$10=$N$10    Binding    0
        $L$11    LE Beginning balances    400    $L$11=$N$11    Binding    0
        $L$12    LE Beginning balances    300    $L$12=$N$12    Binding    0
        $L$13    LE Beginning balances    200    $L$13=$N$13    Binding    0
        $L$14    LE Beginning balances    100    $L$14=$N$14    Binding    0
        $L$15    LE Beginning balances    300    $L$15=$N$15    Binding    0
        $L$16    LE Beginning balances    200    $L$16=$N$16    Binding    0
        $L$17    LE Beginning balances    300    $L$17=$N$17    Binding    0
        $L$18    B5 Beginning balances    400    $L$18=$N$18    Binding    0
        $B$2    P1    360    $B$2>=0    Not Binding    360
        $B$3    P2    20    $B$3>=0    Not Binding    20
        $B$4    P3    400    $B$4>=0    Not Binding    400
        $B$5    P4    380    $B$5>=0    Not Binding    380
        $B$6    P5    50    $B$6>=0    Not Binding    50
        $B$7    P6    300    $B$7>=0    Not Binding    300
        $B$8    P7    250    $B$8>=0    Not Binding    250
        $B$9    P8    400    $B$9>=0    Not Binding    400
        $B$10    P9    20    $B$10>=0    Not Binding    20
        $B$11    P10    400    $B$11>=0    Not Binding    400
        $B$12    P11    380    $B$12>=0    Not Binding    380
        $B$13    P12    50    $B$13>=0    Not Binding    50
        $B$14    B1    90    $B$14>=0    Not Binding    90
        $B$15    B2    350    $B$15>=0    Not Binding    350
        $B$16    B3    70    $B$16>=0    Not Binding    70
        $B$17    B4    270    $B$17>=0    Not Binding    270
        $B$18    B5    350    $B$18>=0    Not Binding    350
        $B$19    B6    0    $B$19>=0    Binding    0
        $B$20    B7    0    $B$20>=0    Binding    0
        $B$21    B8    50    $B$21>=0    Not Binding    50
        $B$22    B9    350    $B$22>=0    Not Binding    350
        $B$23    B10    70    $B$23>=0    Not Binding    70
        $B$24    B11    270    $B$24>=0    Not Binding    270
        $B$25    B12    350    $B$25>=0    Not Binding    350
        $B$26    B13    0    $B$26>=0    Binding    0
Sensitivity Report 1
    Microsoft Excel 15.0 Sensitivity Report
    Worksheet: [30374.xlsx]Sheet1
    Report Created: 07/05/2018 22:38:21
    Variable Cells
                Final    Reduced    Objective    Allowable    Allowable
        Cell    Name    Value    Cost    Coefficient    Increase    Decrease
        $B$2    P1    360    0    15    8.5    1E+30
        $B$3    P2    20    0    25    0.5    3
        $B$4    P3    400    0    20    6.5    1E+30
        $B$5    P4    380    0    25    3    1E+30
        $B$6    P5    50    0    30    1E+30    0.5
        $B$7    P6    300    0    25    6.5    1E+30
        $B$8    P7    250    0    20    2    6.5
        $B$9    P8    400    0    15    6.5    1E+30
        $B$10    P9    20    0    25    0.125    2
        $B$11    P10    400    0    20    6.5    1E+30
        $B$12    P11    380    0    25    3    1E+30
        $B$13    P12    50    0    30    1E+30    0.125
        $B$14    B1    90    0    0.75    1E+30    1E+30
        $B$15    B2    350    0    1.5    8.5    1E+30
        $B$16    B3    70    0    1.5    0.5    3
        $B$17    B4    270    0    1.5    0.5    3
        $B$18    B5    350    0    1.5    0.5    1E+30
        $B$19    B6    0    0    1.5    1E+30    6.5
        $B$20    B7    0    13    1.5    1E+30    13
        $B$21    B8    50    0    1.5    2    6.5
        $B$22    B9    350    0    1.5    2    1E+30
        $B$23    B10    70    0    1.5    0.125    3
        $B$24    B11    270    0    1.5    0.125    3
        $B$25    B12    350    0    1.875    0.125    1E+30
        $B$26    B13    0    31.125    1.125    1E+30    31.125
    Constraints
                Final    Shadow    Constraint    Allowable    Allowable
        Cell    Name    Value    Price    R.H. Side    Increase    Decrease
        $D$6    month 1 production levels    360    0    400    1E+30    40
        $D$7    month 2 production levels    20    0    350    1E+30    330
        $D$8    month 3 production levels    400    -6.5    400    20    280
        $D$9    month 4 production levels    380    -3    380    20    80
        $D$10    month 5 production levels    50    0    400    1E+30    350
        $D$11    month 6 production levels    300    -6.5    300    0    300
        $D$12    month 7 production levels    250    0    300    1E+30    50
        $D$13    month 8 production levels    400    -6.5    400    50    50
        $D$14    month 9 production levels    20    0    350    1E+30    330
        $D$15    month 10 production levels    400    -6.5    400    20    280
        $D$16    month 11 production levels    380    -3    380    20    80
        $D$17    month 12 production...