Consider four binary decision variables: x1, x2, X3, X4 E {0,1}. Suppose that the sum of these decision variables must be equal to an odd number. For instance, setting x, = 1, x, = 1, x3 = 1, and x4 = 0 satisfies the condition while setting x, = 1, x, = 1, x3 = 0, and x4 = 0 does not satisfy the condition. Derive a system of constraints, and potentially additional decision variables, that would eliminate all possible cases that do not satisfy the aforementioned condition.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2) Consider four binary decision variables: x1, x2, X3, X4 E {0,1}. Suppose that the sum of these decision
variables must be equal to an odd number. For instance, setting x, = 1, x, = 1, x3 = 1, and x4 = 0 satisfies
the condition while setting x, = 1, x, = 1, x3 = 0, and x4 = 0 does not satisfy the condition. Derive a
%3D
system of constraints, and potentially additional decision variables, that would eliminate all possible cases
that do not satisfy the aforementioned condition.
Transcribed Image Text:2) Consider four binary decision variables: x1, x2, X3, X4 E {0,1}. Suppose that the sum of these decision variables must be equal to an odd number. For instance, setting x, = 1, x, = 1, x3 = 1, and x4 = 0 satisfies the condition while setting x, = 1, x, = 1, x3 = 0, and x4 = 0 does not satisfy the condition. Derive a %3D system of constraints, and potentially additional decision variables, that would eliminate all possible cases that do not satisfy the aforementioned condition.
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