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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

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
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.
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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