3 Polyhedra in Standard Form(3.1) Convert the following general linear programming problem into standard form:- 2x1+ 3x3maxs.t.2x1-X1x22x22x2X2 ≤ 09Remark It is irrelevant whether the problem is actually feasible or not.X1X1 ≥ 0-x2+++2X33x3TX3X3 ≤02x4X4+ X4+ 2x4IV IA II=124< 2

We have to convert the LPP into standard form Max s.t

Answered: Convert the following general linear…

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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Question

3 Polyhedra in Standard Form
(3.1) Convert the following general linear programming problem into standard form:
- 2x1
+ 3x3
max
s.t.
2x1
-X1
x2
2x2
2x2
X2 ≤ 0
9
Remark It is irrelevant whether the problem is actually feasible or not.
X1
X1 ≥ 0
-
x2
+
+
+
2
X3
3x3
T
X3
X3 ≤0
2x4
X4
+ X4
+ 2x4
IV IA II
=
124
< 2

Expert Solution

Step 1: Introduction of the given problem

We have to convert the LPP into standard form

Max $2 x subscript 1 minus x subscript 2 plus 3 x subscript 3 minus 2 x subscript 4$

s.t

$2 x subscript 1 minus x subscript 2 plus x subscript 3 minus x subscript 4 equals 1 minus x subscript 1 plus 2 x subscript 2 minus 3 x subscript 3 plus x subscript 4 less or equal than 2 x subscript 1 plus 2 x subscript 2 minus x subscript 3 plus 2 x subscript 4 greater or equal than 4 x subscript 1 greater or equal than 0 comma space x subscript 2 less or equal than 0 comma space x subscript 3 less or equal than 0$