2. Rewrite the following linear program in standard form.(1)s.t.min z = -5x1 - 6x2 - 7x3-x1 - 5x2 3x3 ≥ 15-5x1 - 6x2 + 10x3 ≤ 20x1x2x3 = -5x1 ≤ 0, x2 > 0, x3 unconstrained-

Given the linear program:The aim is to convert it into standard form.To rewrite it in standard form,…

Answered: 2. (1) Rewrite the following 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

2. Rewrite the following linear program in standard form.
(1)
s.t.
min z = -5x1 - 6x2 - 7x3
-x1 - 5x2 3x3 ≥ 15
-5x1 - 6x2 + 10x3 ≤ 20
x1x2x3 = -5
x1 ≤ 0, x2 > 0, x3 unconstrained
-

Expert Solution

Step 1: Introduction to the problem and process used

Given the linear program:

$text min: end text z equals negative 5 x subscript 1 minus 5 x subscript 2 minus 3 x subscript 3 greater or equal than 15 text Subject to: end text minus x subscript 1 minus 5 x subscript 2 minus 3 x subscript 3 greater or equal than 15 minus 5 x subscript 1 minus 6 x subscript 2 plus 10 x subscript 3 less or equal than 20 x subscript 1 minus x subscript 2 minus x subscript 3 equals negative 5 x subscript 1 less or equal than 0 comma space x subscript 2 greater or equal than 0 comma space x subscript 3 space text unconstrained end text$

The aim is to convert it into standard form.

To rewrite it in standard form, we need to do the following:

Move the objective function to the right-hand side of the equation.
Add slack variables for all the inequalities.
Replace all the inequalities with equalities by adding artificial variables and subtracting their corresponding coefficients from the objective function.