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
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Question
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.
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