Consider the problem Maximize z = x1 + x2 subject to 2x1 + x2 < 6 X1 + 2x2 < 6 X1 + x2 2 0 (a) Show that the optimal basic solution includes both x1 and x2
Consider the problem Maximize z = x1 + x2 subject to 2x1 + x2 < 6 X1 + 2x2 < 6 X1 + x2 2 0 (a) Show that the optimal basic solution includes both x1 and x2
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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![Consider the problem
Мaximize z %3D Х] + X2
subject to
2x1 + x2 < 6
X1 + 2x2 < 6
X1 + x2 > 0
(a) Show that the optimal basic solution includes both x1 and x2 and that the feasibility
ranges for the two constraints, considered one at a time, are -3 < D1 < 6 and
-3 < D2 < 6.
*(b) Suppose that the two resources are increased simultaneously by A > 0 each. First,
show that the basic solution remains feasible for all A > 0. Next, show that the
100% rule will confirm feasibility only if the increase is in the range 0 < A 3 units.
Otherwise, the rule fails for 3 < A < 6 and does not apply for A > 6.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fa8a196-ad7d-4132-835d-08dfd0e41755%2F017d4f86-1efa-458f-a8b0-3ae94bd51029%2F3ys7a75_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the problem
Мaximize z %3D Х] + X2
subject to
2x1 + x2 < 6
X1 + 2x2 < 6
X1 + x2 > 0
(a) Show that the optimal basic solution includes both x1 and x2 and that the feasibility
ranges for the two constraints, considered one at a time, are -3 < D1 < 6 and
-3 < D2 < 6.
*(b) Suppose that the two resources are increased simultaneously by A > 0 each. First,
show that the basic solution remains feasible for all A > 0. Next, show that the
100% rule will confirm feasibility only if the increase is in the range 0 < A 3 units.
Otherwise, the rule fails for 3 < A < 6 and does not apply for A > 6.
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