asider the following problem: Maximize Z = 4.x1 + 5x2 3.x3 (1) (2) subject to -xị X2 + 2х3 < -20 15x1 + 6x2 + 5x3 < + 3x2 xị 2 0, x2 > 0, æ3 < 0. 50 X1 5x3 < 30 Reformulate the problem so that the goal is "maximizing an objective function," the right-hand-side of each functional constraint is non-negative and each variable has a non-negativity constraint. Construct the phase-1 problem in algebraic/tabular form by introducing slack, excess and/or artificial variables. Define all variables clearly. Work through the phase-1 of the two-phase method in tabular form to demonstrate that the problem has no feasible solutions. In each simplex tableau, identify the current solution for (x1, x2, x3).
asider the following problem: Maximize Z = 4.x1 + 5x2 3.x3 (1) (2) subject to -xị X2 + 2х3 < -20 15x1 + 6x2 + 5x3 < + 3x2 xị 2 0, x2 > 0, æ3 < 0. 50 X1 5x3 < 30 Reformulate the problem so that the goal is "maximizing an objective function," the right-hand-side of each functional constraint is non-negative and each variable has a non-negativity constraint. Construct the phase-1 problem in algebraic/tabular form by introducing slack, excess and/or artificial variables. Define all variables clearly. Work through the phase-1 of the two-phase method in tabular form to demonstrate that the problem has no feasible solutions. In each simplex tableau, identify the current solution for (x1, x2, x3).
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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Please provide detailed explanation.
Transcribed Image Text:Consider the following problem:
Maximize Z
subject to
4.x1 + 5x2
3x3
+ 2x3
15х1 + 622 + 523
5x3 <
(1)
(2)
(3)
-x1
X2
-20
50
X1
+ 3x2
30
Xı > 0, x2 > 0, æ3 < 0.
(a) Reformulate the problem so that the goal is "maximizing an objective function," the
right-hand-side of each functional constraint is non-negative and each variable has a
non-negativity constraint.
(b) Construct the phase-1 problem in algebraic/tabular form by introducing slack, excess
and/or artificial variables. Define all variables clearly.
(c) Work through the phase-1 of the two-phase method in tabular form to demonstrate that
the problem has no feasible solutions. In each simplex tableau, identify the current
solution for (x1, x2, X3).
VI VI VI
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