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: exactly one mall should be constructed among locations 1 and 3
A) $\mathrm{X}_{1}+\mathrm{X}_{3} \leq$ 1
B) $\mathrm{X}_{1}+\mathrm{X}_{3} \geq$1
C) $X_{1}+X_{3}$1
D) $X_{1}+X_{3}=$ 1

Question

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: exactly one mall should be constructed among locations 1 and 3
A) $\mathrm{X}_{1}+\mathrm{X}_{3} \leq$ 1
B) $\mathrm{X}_{1}+\mathrm{X}_{3} \geq$1
C) $X_{1}+X_{3}>$1
D) $X_{1}+X_{3}=$ 1

Quizplus · Accepted Answer

To ensure exactly one mall is constructed either at location 1 or 3, the sum of $X_{1}$ and $X_{3}$ must equal 1. This means one variable is 1 and the other is 0, satisfying the condition.

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