Consider the problemМaximize z %3D Х] + X2subject to2x1 + x2 < 6X1 + 2x2 < 6X1 + x2 > 0(a) Show that the optimal basic solution includes both x1 and x2 and that the feasibilityranges 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 the100% 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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Description: Consider the problemМaximize z %3D Х] + X2subject to2x1 + x2 0(a) Show that the optimal basic solution includes both x1 and x2 and that the feasibilityranges for the two constraints, considered one at a time, are -3 < D1 < 6

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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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Question

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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