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1,1 ≥ 2, 1,2 ≥ 3, 2,1 ≥ 3, 3,1 ≥ 4, 2,2 ≥ 4, 1,3 ≥ 4, 4,1 ≥ 5, 3,2 ≥ 5, 2,3 ≥ 5, 1,4 ≥ 5

1,1 ≥ 2, 1,2 ≥ 3, 2,1 ≥ 3, 3,1 ≥ 4, 2,2 ≥ 4, 1,3 ≥ 4, 4,1 ≥ 5, 3,2 ≥ 5, 2,3 ≥ 5, 1,4 ≥ 5

Advanced Engineering Mathematics
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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Answer question 6. Write each of the following as compactly as possible using summation and "for all" indexed notation.
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, 3,1 ≥ 4, x2,2 ≥ 4, 1,3 ≥ 4, 4,1 ≥ 5, x3,2 ≥ 5, X2,3 ≥ 5, X1,4 ≥ 5 7. min e¹e¹+x2 + e*1+x2+x3 + €²1+x2+x3+x4 +1+₂+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, 4 ≥ 0, x5 ≥ 0. min 1,1 1,2 1,3 + x1,4+2,2 + x2,3 + x2,4 + x3,3 + x3,4 +4,4 s.t. 1,1 2,1 3,1 1,2 + 1,3 + x1,4 ≥ 1 2,2 + 2,3 +2,421 3,2 + x3,3 +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 1,3x2,3 + x3,3 +4,3 ≥ 1 X1,4+x2,4x3,4+X4,4 ≥ 1 1,1 ≥ 0, 1,2 ≥ 0, x1,3 ≥ 0, 1,4 ≥0 2,1 ≥ 0, x2,2 ≥ 0, 2,3 ≥ 0, x2,4 ≥0 3,4 ≥0 3,1 ≥ 0, x3,2 ≥ 0, x3,3 ≥ 0, 4,1 ≥ 0, 4,2 ≥ 0, 4,3 ≥ 0, 4,4 ≥ 0.
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, 3,1 ≥ 4, x2,2 ≥ 4, 1,3 ≥ 4, 4,1 ≥ 5, x3,2 ≥ 5, X2,3 ≥ 5, X1,4 ≥ 5 7. min e¹e¹+x2 + e*1+x2+x3 + €²1+x2+x3+x4 +1+₂+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, 4 ≥ 0, x5 ≥ 0. min 1,1 1,2 1,3 + x1,4+2,2 + x2,3 + x2,4 + x3,3 + x3,4 +4,4 s.t. 1,1 2,1 3,1 1,2 + 1,3 + x1,4 ≥ 1 2,2 + 2,3 +2,421 3,2 + x3,3 +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 1,3x2,3 + x3,3 +4,3 ≥ 1 X1,4+x2,4x3,4+X4,4 ≥ 1 1,1 ≥ 0, 1,2 ≥ 0, x1,3 ≥ 0, 1,4 ≥0 2,1 ≥ 0, x2,2 ≥ 0, 2,3 ≥ 0, x2,4 ≥0 3,4 ≥0 3,1 ≥ 0, x3,2 ≥ 0, x3,3 ≥ 0, 4,1 ≥ 0, 4,2 ≥ 0, 4,3 ≥ 0, 4,4 ≥ 0.
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