In modeling a shopping mall construction problem, there are four potential locations giving rise to four 0-1 decision variables denoted as $X_{1}, X_{2}, X_{3}, X_{4}$, which take a value of 1 if a mall is constructed and 0 otherwise. Identify the correct set of constraint/s to satisfy the following condition/s: if a mall is constructed in location 2, then a mall should be constructed in location 4
A) $\mathrm{X}_{2}-\mathrm{X}_{4} \leq$ 0.
B) $-X_{2}+X_{4} \geq$0.
C) $\mathrm{X}_{2}-\mathrm{X}_{4} \leq$ 0
D) $-\mathrm{X}_{2}+\mathrm{X}_{4} \leq$0

Question

Quizplus · Accepted Answer

If a mall is constructed in location 2, then $X_2 = 1$. To ensure that a mall is also constructed in location 4, we need to enforce the constraint $-X_2 + X_4 \geq 0$. This constraint ensures that if $X_2$ is 1 (i.e., a mall is constructed in location 2), then $X_4$ must also be 1 (i.e., a mall is constructed in location 4).

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In Modeling a Shopping Mall Construction Problem, There Are Four $X_{1}, X_{2}, X_{3}, X_{4}$