Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
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 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
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,
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,
Expert Solution
steps

Step by step

Solved in 5 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS