T (a) Determine whether or not x = (0, 4, 0, 2) is an optimal solution to the following linear program. maximize subject to 9x1 + 3x2 + 5x3 + 22x4 2x1 x2 + 2x3 +6x4≤ 8, 5x1 + 3x2 + x3 + 2x4≤ 16, 4x1 + x2x3 + 3x4≤ 12, X1, X2, X3, X4 ≥0 - (b) Determine whether x¹ = (0, 2, 3) is an optimal solution to the following linear program. maximize subject to ₁ + X2 + X3 2x1 + 7x2 + x3 ≤ 8, x1 + 3x2 + 3x3 ≤ 7, 2x1 +4x3 ≤ 6, x1 + 3x2 + x3 ≤ 9, X1, X2, X3 20
T (a) Determine whether or not x = (0, 4, 0, 2) is an optimal solution to the following linear program. maximize subject to 9x1 + 3x2 + 5x3 + 22x4 2x1 x2 + 2x3 +6x4≤ 8, 5x1 + 3x2 + x3 + 2x4≤ 16, 4x1 + x2x3 + 3x4≤ 12, X1, X2, X3, X4 ≥0 - (b) Determine whether x¹ = (0, 2, 3) is an optimal solution to the following linear program. maximize subject to ₁ + X2 + X3 2x1 + 7x2 + x3 ≤ 8, x1 + 3x2 + 3x3 ≤ 7, 2x1 +4x3 ≤ 6, x1 + 3x2 + x3 ≤ 9, X1, X2, X3 20
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:2. For each of the following questions, justify your answer using complementary slack-
ness and if the given solution is optimal, give an optimal solution to the dual as
well.
(a) Determine whether or not x¹ = (0, 4, 0, 2) is an optimal solution to the following
linear program.
maximize 9x1 + 3x2 + 5x3 + 22x4
subject to
2x1 x2 + 2x3 + 6x4≤ 8,
5x1 + 3x2 + x3 + 2x4≤ 16,
4x1 + x2x3 + 3x4 ≤ 12,
X1, X2, X3, X4 ≥ 0
(b) Determine whether x¹ = (0, 2, 3) is an optimal solution to the following linear
program.
maximize
subject to
₁ + X2 + X3
2x1 + 7x2 + x3 ≤ 8,
x1 + 3x2 + 3x3 ≤ 7,
2x1
+4x3 ≤ 6,
x1 + 3x2 + x3 ≤ 9,
X1, X2, X3 ≥ 0
Transcribed Image Text:2. For each of the following questions, justify your answer using complementary slack-
ness and if the given solution is optimal, give an optimal solution to the dual as
well.
(a) Determine whether or not x¹ = (0, 4, 0, 2) is an optimal solution to the following
linear program.
maximize
subject to
9x1 + 3x2 + 5x3 + 22x4
2x1 - x2 + 2x3 + 6x4≤ 8,
5x1 + 3x2 + x3 + 2x4≤ 16,
4x1 + x2x3 + 3x4≤ 12,
X1, X2, X3, X4 ≥ 0
(b) Determine whether x¹ = (0, 2, 3) is an optimal solution to the following linear
program.
maximize
subject to
x1 + x2 + x3
2x1 + 7x2 + x3 ≤ 8,
x1 + 3x2 + 3x3 ≤ 7,
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