Consider the feasible region in R³ defined by the inequalities x₁ + 2x2x3 ≥ 3, x2 + 3x3 ≤ 2, and x₁20, x₂ ≥ 0, x3 ≥ 0. (a) Introduce non-negative slack variables x4 and x5 and write down the corresponding linear system. (b) Find the basic solution obtained by making ₁ and ₂ basic vari- ables. Is this basic solution feasible? (c) Find the basic solution obtained by making ₁ and x3 basic vari- ables. Is this basic solution feasible?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Algebra
Consider the feasible region in R³ defined by the inequalities
x₁ + 2x₂x3 ≥ 3,
x2 + 3x3 ≤ 2,
and x₁0, x2 ≥ 0, x3 ≥ 0.
(a) Introduce non-negative slack variables x4 and x5 and write down
the corresponding linear system.
(b) Find the basic solution obtained by making î₁ and 2 basic vari-
ables. Is this basic solution feasible?
(c) Find the basic solution obtained by making ₁ and x3 basic vari-
ables. Is this basic solution feasible?
Transcribed Image Text:Algebra Consider the feasible region in R³ defined by the inequalities x₁ + 2x₂x3 ≥ 3, x2 + 3x3 ≤ 2, and x₁0, x2 ≥ 0, x3 ≥ 0. (a) Introduce non-negative slack variables x4 and x5 and write down the corresponding linear system. (b) Find the basic solution obtained by making î₁ and 2 basic vari- ables. Is this basic solution feasible? (c) Find the basic solution obtained by making ₁ and x3 basic vari- ables. Is this basic solution feasible?
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