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Or3 Odt

The document describes two linear programming problems. The first problem involves minimizing an objective function subject to three constraints, and asks to reformulate it into standard form and solve it using both the Big M method and two-phase method. The second problem involves maximizing an objective function subject to two constraints and has no feasible solution, and asks to demonstrate this graphically and using the Big M method and two-phase method.

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Wajini Lakshika
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51 views1 page

Or3 Odt

The document describes two linear programming problems. The first problem involves minimizing an objective function subject to three constraints, and asks to reformulate it into standard form and solve it using both the Big M method and two-phase method. The second problem involves maximizing an objective function subject to two constraints and has no feasible solution, and asks to demonstrate this graphically and using the Big M method and two-phase method.

Uploaded by

Wajini Lakshika
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as ODT, PDF, TXT or read online on Scribd
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Operational Research

1. Consider the following problem:

minimize Z = 2x1 + 3x2 + x3,


subject to
x1 + 4x2 + 2x3 ≥ 8
3x1 + 2x2 ≥ 6
and
xj ≥ 0, j = 1, 2, 3.
(a) Reformulate this problem to fit the standard form for a linear programming model
(b) Using the Big M method, work through the simplex method step by step to solve the problem.
(c) Using the two-phase method, work through the simplex method step by step to solve the problem.
(d) Compare the sequence of BF solutions obtained in parts (b) and (c). Which of these solutions are
feasible only for the artificial problem obtained by introducing artificial variables and which are
actually feasible for the real problem?

2. Consider the following problem.


maximize Z = 90x1 + 70x2,
subject to
2x1 + x2 ≤ 2
x1 − x2 ≥ 2
and x1 ≥ 0, x2 ≥ 0.

(a) Demonstrate graphically that this problem has no feasible solutions.


(b) Using the Big M method, work through the simplex method step by step to demonstrate that the
problem has no feasible solutions.
(c) Repeat part (b) when using phase 1 of the two-phase method.

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