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 + x₂ 3 + 3x4≤ 12, T1, T2, T3, T4 20 (b) Determine whether x¹ = (0,,) is an optimal solution to the following linear program. maximize subject to ₁+₂+£3 21 +7x₂ + x3 ≤ 8, x₁ + 3x₂ + 3x3 ≤7, 2x1 +4x3 ≤ 6, ₁+ 3x₂ + x3 ≤ 9, I1, I2, I3 20 (c) Determine whether x¹ = (0,2,0) is an optimal solution to the following linear program. maximize subject to 3x₁ + 8x₂ + x3 2x₁ +82 +2£3 ≤ 4, 3x₁ +4x₂+2x3 ≤ 4, 1x₁ + 2x2 + 1x3 ≤ 1, I1, I2, I3 20
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 + x₂ 3 + 3x4≤ 12, T1, T2, T3, T4 20 (b) Determine whether x¹ = (0,,) is an optimal solution to the following linear program. maximize subject to ₁+₂+£3 21 +7x₂ + x3 ≤ 8, x₁ + 3x₂ + 3x3 ≤7, 2x1 +4x3 ≤ 6, ₁+ 3x₂ + x3 ≤ 9, I1, I2, I3 20 (c) Determine whether x¹ = (0,2,0) is an optimal solution to the following linear program. maximize subject to 3x₁ + 8x₂ + x3 2x₁ +82 +2£3 ≤ 4, 3x₁ +4x₂+2x3 ≤ 4, 1x₁ + 2x2 + 1x3 ≤ 1, I1, I2, I3 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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,