the nearest integer solution and check whether it is feasible. Then enumerate all the rounded solutions by rounding this solution for the LP relaxation in all possible ways (i.e., by rounding each noninteger value both up and down). For each rounded solution, check for feasibility and, if feasible, calcu- late Z. Are any of these feasible rounded solutions optimal for the IP problem? 12.5-2. Follow the instructions of Prob. 12.5-1 for the following IP problem: Maximize z= 220x, + 80x, subject to 5x, + 2x S 16 2x, - x25 4 -X, + 2x,s 4 and X 20, x2 20 X, X2 are integers.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) Solve this problem graphically.
(b) Solve the LP relaxation graphically. Round this solution to
the nearest integer solution and check whether it is feasible.
Then enumerate all the rounded solutions by rounding this
solution for the LP relaxation in all possible ways (i.e., by
rounding each noninteger value both up and down). For each
rounded solution, check for feasibility and, if feasible, calcu-
late Z. Are any of these feasible rounded solutions optimal for
the IP problem?
12.5-2. Follow the instructions of Prob. 12.5-1 for the following IP
problem:
Maximize
Z = 220x, + 80x,
subject to
5x, + 2x < 16
2x, - x2s 4
-X + 2x s 4
and
X 2 0,
x2 20
X1, X2 are integers.
Transcribed Image Text:(a) Solve this problem graphically. (b) Solve the LP relaxation graphically. Round this solution to the nearest integer solution and check whether it is feasible. Then enumerate all the rounded solutions by rounding this solution for the LP relaxation in all possible ways (i.e., by rounding each noninteger value both up and down). For each rounded solution, check for feasibility and, if feasible, calcu- late Z. Are any of these feasible rounded solutions optimal for the IP problem? 12.5-2. Follow the instructions of Prob. 12.5-1 for the following IP problem: Maximize Z = 220x, + 80x, subject to 5x, + 2x < 16 2x, - x2s 4 -X + 2x s 4 and X 2 0, x2 20 X1, X2 are integers.
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