Formulate the dual problem for the following linear programming model. 1. Minimize: C = 10x1 + 8x2 + 12x3 Subject to: 5xı +3x2 + 6x3 < 153 Maximize: P = 2x1 + x2+ x3 < 50 Subject to: x1, x2, X3 2 0
Formulate the dual problem for the following linear programming model. 1. Minimize: C = 10x1 + 8x2 + 12x3 Subject to: 5xı +3x2 + 6x3 < 153 Maximize: P = 2x1 + x2+ x3 < 50 Subject to: x1, x2, X3 2 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Section Exercise 4.2
Formulate the dual problem for the following linear programming model.
1. Minimize: C = 10x1 + 8x2+ 12x3
Subject to: 5x1 + 3x2 + 6x3 < 153
%3D
Maximize: P =
2x1 + x2+ x3 < 50
Subject to:
X1, x2, x3 20
M =
M
2. Maximize: P = 40x1 + 20x2
Subject to:
Minimize: C=
X2<10
Subject to:
X1 +
x2<18
2r1 + 5x2 <60
3x1 + x2<44
x1, x2 20
%3D
M =
Maximize: P =
3. Minimize: C = 12x1 + 6x2+ 14x3
Subject to: 2x1 + 3x2 2 12
x1 +4x3 = 16
3x1 + x3< 23
%3D
Subject to:
x1, x2, x32 0
M =
M =
Chapter 4: Duality and Sensitivity Analysis
Page 117
TIH
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Section Exercise 4.2A
Solve the primal problem using duality and determine the primal and dual solution.
1. Maximize: P 8x1 + 6x2
Subject to:
%3D
Minimize: C =
2x23
2x1 +x254
Subject to:
4xn S8
x1, x2 20
Solution:
Tableau 1
BV
yi
y2
ya
S1
S2
RHS
P
Tableau 2
BV
y1
y2
ys
S1
S2
RHS
Tableau 3
BV
y2
y3
Si
S2
P
RHS
yi
Si =
Dual Solution: yı =
%3D
S2 =
Primal Solution: x1D
Page 119
Chapter 4: Duality and Sensitivity Analysis
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