B₂ = {(2₂1 X12 X22 |xij≥0 for i, j = 1, 2, X11 + 12 = 2, X21 + x22 = 2, x11 + x21 = 1.5, x12 + x22 = 2.5 (6) Let B₂ to be the set described in the screenshot attached Suppose cij are real numbers such that C11C22 C12 + C21 > 0. Consider the following LPP: maximize: C11x11 +C12x12 + C2121 + C2222 x11 X12 X21 X22 € B₂ subject to: (a) Write this problem in canonical form {x = (x11, 212, 21, 22) € R4 | Ax = b, x>0}. Hint: A should be a 3 x 4 matrix (after you eliminate one row which is linearly dependent on the others). (b) List all BFS. (c) Which BFS * has the maximum cost for this LPP? For the maximizer r* show that for all basic directions D: at r* the reduced cost.
B₂ = {(2₂1 X12 X22 |xij≥0 for i, j = 1, 2, X11 + 12 = 2, X21 + x22 = 2, x11 + x21 = 1.5, x12 + x22 = 2.5 (6) Let B₂ to be the set described in the screenshot attached Suppose cij are real numbers such that C11C22 C12 + C21 > 0. Consider the following LPP: maximize: C11x11 +C12x12 + C2121 + C2222 x11 X12 X21 X22 € B₂ subject to: (a) Write this problem in canonical form {x = (x11, 212, 21, 22) € R4 | Ax = b, x>0}. Hint: A should be a 3 x 4 matrix (after you eliminate one row which is linearly dependent on the others). (b) List all BFS. (c) Which BFS * has the maximum cost for this LPP? For the maximizer r* show that for all basic directions D: at r* the reduced cost.
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
![B₂ {(₂1
X12
X22
| Xij ≥ 0 for i, j = 1, 2, X11 + 12 = 2, X21 + x22 = 2, X11 + x21
(6) Let B₂ to be the set described in the screenshot attached Suppose Cij are real numbers such that
C11C22 C12 + C21 > 0. Consider the following LPP:
maximize: C11x11 + C12x12 + C21%21+ C22X22
subject to: (#11 #12) € B₂
X21
= 1.5, x12 + x22 = 2.
(a) Write this problem in canonical form {x = (x11, 12, X21, X22) € R4 | Ax = b, x ≥ 0}.
Hint: A should be a 3 x 4 matrix (after you eliminate one row which is linearly
dependent on the others).
(b) List all BFS.
Which BFS x* has the maximum cost for this LPP?
2.5}.
For the maximizer x*, show that for all basic directions D₁ at x* the reduced cost
Cj = c² Dj ≤ 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa69386ea-ae53-412f-8880-26572739b6ec%2Ff7714665-5164-4599-888c-84d818558897%2Fcznvvk_processed.png&w=3840&q=75)
Transcribed Image Text:B₂ {(₂1
X12
X22
| Xij ≥ 0 for i, j = 1, 2, X11 + 12 = 2, X21 + x22 = 2, X11 + x21
(6) Let B₂ to be the set described in the screenshot attached Suppose Cij are real numbers such that
C11C22 C12 + C21 > 0. Consider the following LPP:
maximize: C11x11 + C12x12 + C21%21+ C22X22
subject to: (#11 #12) € B₂
X21
= 1.5, x12 + x22 = 2.
(a) Write this problem in canonical form {x = (x11, 12, X21, X22) € R4 | Ax = b, x ≥ 0}.
Hint: A should be a 3 x 4 matrix (after you eliminate one row which is linearly
dependent on the others).
(b) List all BFS.
Which BFS x* has the maximum cost for this LPP?
2.5}.
For the maximizer x*, show that for all basic directions D₁ at x* the reduced cost
Cj = c² Dj ≤ 0.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 6 steps with 59 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
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…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)