Given the following linear programming model; Who are the basic variables on the initial board? Min Z = 8 X1 - 12 X2 + 4 X3 Hold it: X1 + X2 + X3> = 30 2 X1 + 3X2 + X3> = 12 X1> = 0; X2> = 0; X3> = 0 Select one: a. h1; h2; A1; A2 b. h1; h2 c. X1; X2 d. All e. A1; A2

Given the following linear programming model; Who are the basic variables on the initial board? Min Z = 8 X1 - 12 X2 + 4 X3 Hold it: X1 + X2 + X3> = 30 2 X1 + 3X2 + X3> = 12 X1> = 0; X2> = 0; X3> = 0 Select one: a. h1; h2; A1; A2 b. h1; h2 c. X1; X2 d. All e. A1; A2

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

Given the following linear programming model; Who are the basic variables on the initial board?

Min Z = 8 X1 - 12 X2 + 4 X3

Hold it:

X1 + X2 + X3> = 30

2 X1 + 3X2 + X3> = 12

X1> = 0; X2> = 0; X3> = 0

Select one:

a.
h1; h2; A1; A2

b.
h1; h2

c.
X1; X2

d.
All

e.
A1; A2

Expert Solution

Step 1

Given problem is

$m i n Z = 8 x_{1} - 12 x_{2} + 4 x_{3} S u b j e c t t o x_{1} + x_{2} + x_{3} \geq 30 2 x_{1} + 3 x_{2} + x_{3} \geq 12$

Since both the constraints are $\geq$ type, so we will substract surplus variables and add artificial variables in both constraints.

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