Microsoft Excel 15.
20 Answer Report
Worksheet: [hw1(3).xlsx]Sheet1
Report Created: 2016/10/29 8:37:25 下午
Result: Solver found a solution. All constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.233443 Seconds.
Iterations: 10 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 1E-06
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Solve Without Integer Constrain
Objective Cell (Min)
Cell Name Original Value Final Value
$R$4 Cost Sum 0 6.4627906977
Variable Cells
$B$3 Variables 𝛽
Cell Name Original Value Final Value Integer
0 0.2790697674 Contin
$D$3 Variables 𝛆1+
$C$3 Variables α 0 1 Contin
$E$3 Variables 𝛆1-
0 0 Contin
$F$3 Variables 𝛆2+
0 0 Contin
$G$3 Variables 𝛆2-
0 0.3813953488 Contin
$H$3 Variables 𝛆3+
0 0 Contin
$I$3 Variables 𝛆3-
0 0 Contin
$J$3 Variables 𝛆4+
0 0.3976744186 Contin
$K$3 Variables 𝛆4-
0 0 Contin
$L$3 Variables 𝛆5+
0 0 Contin
$M$3 Variables 𝛆5-
0 0.4534883721 Contin
$N$3 Variables 𝛆6+
0 0 Contin
$O$3 Variables 𝛆6-
0 4.4069767442 Contin
$P$3 Variables 𝛆7+
0 0 Contin
$Q$3 Variables 𝛆7-
0 0 Contin
0 0.823255814 Contin
Constraints
$R$6 𝛆1 Sum
Cell Name Cell Value Formula Status Slack
$R$7 𝛆2 Sum
1 $R$6=$T$6 Binding 0
$R$8 𝛆3 Sum
1.8 $R$7=$T$7 Binding 0
1.3 $R$8=$T$8 Binding 0
𝛆4 Sum
𝛆5 Sum
$R$9 2.2 $R$9=$T$9 Binding 0
𝛆6 Sum
$R$10 3.1 $R$10=$T$10 Binding 0
𝛆7 Sum
$R$11 7.5 $R$11=$T$11 Binding 0
$R$12 2.8 $R$12=$T$12 Binding 0
Without Integer Constraints, Assume NonNegative
Microsoft Excel 15.20 Sensitivity Report
Worksheet: [hw1(3).xlsx]Sheet1
Report Created: 2016/10/29 8:37:26 下午
Variable Cells
Final Reduced Objective Allowable Allowable
Variables 𝛽
Cell Name Value Cost Coefficient Increase Decrease
$B$3 0.2790697674 0 0 3 1.3
Variables 𝛆1+
$C$3 Variables α 1 0 0 1.3023255814 0.6976744186
Variables 𝛆1-
$D$3 0 1.3023255814 1 1E+030 1.3023255814
Variables 𝛆2+
$E$3 0 0.6976744186 1 1E+030 0.6976744186
Variables 𝛆2-
$F$3 0.3813953488 0 1 0.8666666667 2
Variables 𝛆3+
$G$3 0 2 1 1E+030 2
Variables 𝛆3-
$H$3 0 2 1 1E+030 2
Variables 𝛆4+
$I$3 0.3976744186 0 1 2.92 0.52
Variables 𝛆4-
$J$3 0 1.6976744186 1 1E+030 1.6976744186
Variables 𝛆5+
$K$3 0 0.3023255814 1 1E+030 0.3023255814
Variables 𝛆5-
$L$3 0.4534883721 0 1 0.2203389831 1.2372881356
Variables 𝛆6+
$M$3 0 2 1 1E+030 2
Variables 𝛆6-
$N$3 4.4069767442 0 1 0.1733333333 0.9375
Variables 𝛆7+
$O$3 0 2 1 1E+030 2
Variables 𝛆7-
$P$3 0 2 1 1E+030 2
$Q$3 0.823255814 0 1 0.5882352941 0.1382978723
Constraints
Final Shadow Constraint Allowable Allowable
𝛆1 Sum
Cell Name Value Price R.H. Side Increase Decrease
𝛆2 Sum
$R$6 1 -0.3023255814 1 0.5857142857 0.95
𝛆3 Sum
$R$7 1.8 1 1.8 1E+030 0.3813953488
𝛆4 Sum
$R$8 1.3 -1 1.3 0.3976744186 1E+030
𝛆5 Sum
$R$9 2.2 -0.6976744186 2.2 0.3305084746 0.3765957447
𝛆6 Sum
$R$10 3.1 1 3.1 1E+030 0.4534883721
𝛆7 Sum
$R$11 7.5 1 7.5 1E+030 4.4069767442
$R$12 2.8 -1 2.8 0.823255814 1E+030
Microsoft Excel 15.20 Answer Report
Worksheet: [hw1(3).xlsx]Sheet1
Report Created: 2016/10/29 8:41:18 下午
Result: Solver found a solution. All constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0.197269 Seconds.
Iterations: 9 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Solve Without Integer Constrain
Objective Cell (Min)
Cell Name Original Value Final Value
$E$17 Cost Sum 0 2.55652173913
Variable Cells
$B$16 Variables 𝛽
Cell Name Original Value Final Value Integer
0 0.21739130435 Contin
$D$16 Variables 𝛆
$C$16 Variables α 0 3.31304347826 Contin
0 2.55652173913 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$E$19 Positive Sum 5.86956521739 $E$19>=$G$19 Not Binding 4.8695652174
$E$20 Positive Sum 6.19565217391 $E$20>=$G$20 Not Binding 4.3956521739
$E$21 Positive Sum 6.41304347826 $E$21>=$G$21 Not Binding 5.1130434783
$E$22 Positive Sum 6.80434782609 $E$22>=$G$22 Not Binding 4.6043478261
$E$23 Positive Sum 7.15217391304 $E$23>=$G$23 Not Binding 4.052173913
$E$24 Positive Sum 7.5 $E$24>=$G$24 Binding 0
$E$25 Positive Sum 7.91304347826 $E$25>=$G$25 Not Binding 5.1130434783
$E$26 Negative Sum 0.75652173913 $E$26<=$G$26 Not Binding 0.2434782609
$E$27 Negative Sum 1.08260869565 $E$27<=$G$27 Not Binding 0.7173913043
$E$28 Negative Sum 1.3 $E$28<=$G$28 Binding 0
$E$29 Negative Sum 1.69130434783 $E$29<=$G$29 Not Binding 0.5086956522
$E$30 Negative Sum 2.03913043478 $E$30<=$G$30 Not Binding 1.0608695652
$E$31 Negative Sum 2.38695652174 $E$31<=$G$31 Not Binding 5.1130434783
$E$32 Negative Sum 2.8 $E$32<=$G$32 Binding 0
Without Integer Constraints, Assume NonNegative
Microsoft Excel 15.20 Sensitivity Report
Worksheet: [hw1(3).xlsx]Sheet1
Report Created: 2016/10/29 8:41:18 下午
Variable Cells
Final Reduced Objective Allowable Allowable
$B$16 Variables 𝛽
Cell Name Value Cost Coefficient Increase Decrease
0.2173913043 0 0 2.5 0.95
$D$16 Variables 𝛆
$C$16 Variables α 3.3130434783 0 0 0.1124260355 0.5
2.5565217391 0 1 1E+030 1
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$E$19 Positive Sum 5.8695652174 0 1 4.8695652174 1E+030
$E$20 Positive Sum 6.1956521739 0 1.8 4.3956521739 1E+030
$E$21 Positive Sum 6.4130434783 0 1.3 5.1130434783 1E+030
$E$22 Positive Sum 6.8043478261 0 2.2 4.6043478261 1E+030
$E$23 Positive Sum 7.152173913 0 3.1 4.052173913 1E+030
$E$24 Positive Sum 7.5 0.5 7.5 1E+030 4.052173913
$E$25 Positive Sum 7.9130434783 0 2.8 5.1130434783 1E+030
$E$26 Negative Sum 0.7565217391 0 1 1E+030 0.2434782609
$E$27 Negative Sum 1.0826086957 0 1.8 1E+030 0.7173913043
$E$28 Negative Sum 1.3 -0.1376811594 1.3 0.1787234043 2.7053254438
$E$29 Negative Sum 1.6913043478 0 2.2 1E+030 0.5086956522
$E$30 Negative Sum 2.0391304348 0 3.1 1E+030 1.0608695652
$E$31 Negative Sum 2.3869565217 0 7.5 1E+030 5.1130434783
$E$32 Negative Sum 2.8 -0.3623188406 2.8 1.95 0.672
𝛽 𝛆1- 𝛆2-
Slope Intersept
α 𝛆1+ 𝛆2+
Variables 0.27906977 1 0 0 0.38139535 0
Cost 0 0 1 1 1 1
𝛆1
Constraints
𝛆2
0 1 1 -1
𝛆3
1.5 1 1 -1
𝛆4
2.5 1
𝛆5
4.3 1
𝛆6
5.9 1
𝛆7
7.5 1
9.4 1
𝛽
Slope Intersept
α 𝛆 Sum RHS
Variables 0.2173913 3.31304348 2.55652174
Cost 0 0 1 2.55652174 Min
Constraints
Positive 0 1 1 5.86956522 >= 1
Positive 1.5 1 1 6.19565217 >= 1.8
Positive 2.5 1 1 6.41304348 >= 1.3
Positive 4.3 1 1 6.80434783 >= 2.2
Positive 5.9 1 1 7.15217391 >= 3.1
Positive 7.5 1 1 7.5 >= 7.5
Positive 9.4 1 1 7.91304348 >= 2.8
Negative 0 1 -1 0.75652174 <= 1
Negative 1.5 1 -1 1.0826087 <= 1.8
Negative 2.5 1 -1 1.3 <= 1.3
Negative 4.3 1 -1 1.69130435 <= 2.2
Negative 5.9 1 -1 2.03913043 <= 3.1
Negative 7.5 1 -1 2.38695652 <= 7.5
Negative 9.4 1 -1 2.8 <= 2.8
𝛆3+ 𝛆3- 𝛆4+ 𝛆4- 𝛆5+ 𝛆5- 𝛆6+
0 0.39767442 0 0 0.45348837 0 4.40697674
1 1 1 1 1 1 1
1 -1
1 -1
1 -1
1
L2 Norm
8
7
6
5
f(x) = 0.421261985512708 x + 0.942678892936398
4 R² = 0.41715716892159
Y
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
X
𝛆6- 𝛆7+ 𝛆7- Sum RHS
0 0 0.82325581
1 1 1 6.4627907 Min
1= 1
1.8 = 1.8
1.3 = 1.3
2.2 = 2.2
3.1 = 3.1
-1 7.5 = 7.5
1 -1 2.8 = 2.8
