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Problem Set 3

1) The document contains the primal and dual problems of a linear program with two variables (x1, x2) and two constraints. 2) The primal problem has an objective of 5x1 + 3x2 with constraints of 1.6666x1 + 2.6666x2 <= 16.3333 and 2x1 + x2 <= 6. 3) The dual problem has an objective of 6y1 + 7y2 with constraints of 2.3333y1 + 0.3333y2 <= 16.3333, 2y1 + y2 >= 5, and y1 + 1.6666y2 >= 1.

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60 views5 pages

Problem Set 3

1) The document contains the primal and dual problems of a linear program with two variables (x1, x2) and two constraints. 2) The primal problem has an objective of 5x1 + 3x2 with constraints of 1.6666x1 + 2.6666x2 <= 16.3333 and 2x1 + x2 <= 6. 3) The dual problem has an objective of 6y1 + 7y2 with constraints of 2.3333y1 + 0.3333y2 <= 16.3333, 2y1 + y2 >= 5, and y1 + 1.6666y2 >= 1.

Uploaded by

HariSharanPanjwani
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
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PRIMAL

x1 x2 x3
Objective function 5 3 1
1.666667 2.666667 0 16.33333

Constraints 2 1 1 6 <= 6
1 2 1 7 <= 7
DUAL
y1 y2
Objective function 6 7
2.333333 0.333333 16.33333

Constraints 2 1 5 >= 5
1 2 3 >= 3
1 1 2.666667 >= 1
Microsoft Excel 15.0 Sensitivity Report
Worksheet: [Book1]problem 2
Report Created: 17-09-2019 8.10.17 PM

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$M$4 y1 2.3333333333 0 6 8 2.5
$N$4 y2 0.3333333333 0 7 5 4

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$P$6 Constraints 5 1.6666666667 5 1 3.5
$P$7 <= 3 2.6666666667 3 7 0.5
$P$8 2.6666666667 0 1 1.6666666667 1E+030
PRIMAL
x1 x2
Objective Function 4 1
4.666667 0.666667 19.33333

Constraints 1 2 6= 6
1 -1 4 >= 3
2 1 10 <= 10
Microsoft Excel 15.0 Sensitivity Report
Worksheet: [Problem Set 3.xlsx]Q3
Report Created: 17-09-2019 8.39.58 PM

Variable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$C$4 x1 4.6666666667 0 4 1E+030 3.5
$D$4 x2 0.6666666667 0 1 7 1E+030

Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$F$6 Constraints 6 -0.6666666667 6 1 1
$F$7 4 0 3 1 1E+030
$F$8 10 2.3333333333 10 2 1

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