min e+ e1+₂ +€²1+x2+x3 +²1+x2+x3+x4 +²1+2+3+4+x5 s.t. x1 ≥ ₂ X2 X3 X3 X4 X4 X5 x1 + x2 + x3 + x4+x5 ≤ 1 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0, x5 ≥ 0.
min e+ e1+₂ +€²1+x2+x3 +²1+x2+x3+x4 +²1+2+3+4+x5 s.t. x1 ≥ ₂ X2 X3 X3 X4 X4 X5 x1 + x2 + x3 + x4+x5 ≤ 1 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0, x5 ≥ 0.
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
Answer question 7 or 8 or both. Write each of the following as compactly as possible using summation and "for all" indexed notation.
Transcribed Image Text:5.
x1 - x₂ ≤ 1
x1 + x2x3 ≤ 2
X1 + x2 + x3x4≤3
8.
X₁ + x2 + x3 + x4 x5 ≤ 4
x₁ + x2 + x3 + x4 + x5 x6 ≤ 5
x₁ + x2 + x3 +x4+x5 + x6 x7 ≤ 6
6. x1,1 ≥ 2, 1,2 ≥ 3, 2,1 ≥ 3, x3,1 ≥ 4, x2,2 ≥ 4, 1,3 ≥ 4, x4,1 ≥ 5, x3,2 ≥ 5, x2,3 ≥ 5, x1,4 ≥ 5
7.
min e¹¹ +¹+x2 + e*1+x2+x3 + €²1+x2+x3+x4 +1+x₂+3+4+*5
s.t.
21 ΣΤ2
x2 > X3
X3 X4
X4 X5
x₁ + x2 + x3 + x4+x5 ≤ 1
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0, x5 ≥ 0.
min 1,1 1,2 + x1,3 + x1,4+x2,2 + x2,3 + x2,4 + x3,3 +3,4 +4,4
s.t.
1,2 + 1,3 +x1,4 ≥ 1
2,2 + 2,3 +2,421
+3,2+3,3+3.4 ≥ 1
X4,1 + x4,2x4,3+x4,4 ≥ 1
1,12,1 + x3,1 + x4,1 ≥ 1
1,2 +2,2 + x3,2 + x4,2 ≥ 1
1,3 + x2,3 + x3,3 +4,3 ≥ 1
X1,4+x2,4x3,4+X4,4 ≥ 1
1,1 ≥ 0, 1,2 ≥ 0, x1,3 ≥ 0,
2,1 0, 2,2 ≥ 0, 2,3 ≥ 0,
3,1 ≥ 0,
3,2 ≥ 0, x3,3 ≥ 0,
4,1 0,
4,2 ≥ 0, x4,3 ≥ 0,
1,1
2,1
3,1
1,4 ≥0
2,4 ≥ 0
3,4 ≥ 0
4,4 ≥ 0.
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