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1. Consider the problem of Maximize z = 2r +9r2 Subject to 21 + S 20 I1 +5r2 S 24 a 2 0 and integral (a) Using the simplex algorithm, show that the optimal value of the problem without integral constraints is attained at (8+,3+ ). (b) Show that (8, 3) is a feasible solution to the constraints of the problem.

1. Consider the problem of Maximize z = 2r +9r2 Subject to 21 + S 20 I1 +5r2 S 24 a 2 0 and integral (a) Using the simplex algorithm, show that the optimal value of the problem without integral constraints is attained at (8+,3+ ). (b) Show that (8, 3) is a feasible solution to the constraints of the problem.

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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1. Consider the problem of Maximize z = 2r + 9x2 Subject to +x2 < 20 +5x2 < 24 2 2 0 and integral (a) Using the simplex algorithm, show that the optimal value of the problem without integral constraints is attained at (8+,3+ ). (b) Show that (8,3) is a feasible solution to the constraints of the problem. (c) Show graphically that the optimal solution to the original integrally restricted variable problem is at (4,4). Thus showing that simply rounding non-integral solutions to feasible integral solutions will not always give the optimal integral solutions.
Transcribed Image Text:1. Consider the problem of Maximize z = 2r + 9x2 Subject to +x2 < 20 +5x2 < 24 2 2 0 and integral (a) Using the simplex algorithm, show that the optimal value of the problem without integral constraints is attained at (8+,3+ ). (b) Show that (8,3) is a feasible solution to the constraints of the problem. (c) Show graphically that the optimal solution to the original integrally restricted variable problem is at (4,4). Thus showing that simply rounding non-integral solutions to feasible integral solutions will not always give the optimal integral solutions.
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