In a plant location problem with 5 potential locations, each with an associated 0-1 decision variable, $X_{1}$, $\mathrm{X}_{2}, \mathrm{X}_{3}, \mathrm{X}_{4}$, and $\mathrm{X}_{5}$, which take a value of 1 if a plant is located in that location and 0 otherwise, the constraint to make sure that exactly 3 plants are put up will be A) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5}3.0$ B) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5} \geq 3.0$ C) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5}=3.0$ D) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5} \leq 3.0$ E) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5}

Question

In a plant location problem with 5 potential locations, each with an associated 0-1 decision variable, $X_{1}$, $\mathrm{X}_{2}, \mathrm{X}_{3}, \mathrm{X}_{4}$, and $\mathrm{X}_{5}$, which take a value of 1 if a plant is located in that location and 0 otherwise, the constraint to make sure that exactly 3 plants are put up will be
A) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5}>3.0$
B) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5} \geq 3.0$
C) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5}=3.0$
D) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5} \leq 3.0$
E) $X_{1}+X_{2}+X_{3}+X_{4}+X_{5}<3.0$

Quizplus · Accepted Answer

The constraint $X_{1}+X_{2}+X_{3}+X_{4}+X_{5}=3.0$ ensures that exactly 3 out of the 5 potential locations are selected for placing plants, as it requires the sum of the decision variables to equal 3.

In a Plant Location Problem with 5 Potential Locations, Each X1X_{1}X1​

In a Plant Location Problem with 5 Potential Locations, Each $X_{1}$