A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A–J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model: Min 100x1 + 120x2 + 90x3 + 135x4 +75x5 + 85x6 + 110x7 + 135x8 s.t.x1 + x2 + x5 + x7 ≥ 1 {Neighborhood A constraint} x1 + x2 + x3 ≥ 1 {Neighborhood B constraint} x5 + x6 + x8 ≥ 1 {Neighborhood C constraint} x1 + x4 + x7 ≥ 1 {Neighborhood D constraint} x2 + x3 + x7 ≥ 1 {Neighborhood E constraint} x3 + x4 + x8 ≥ 1 {Neighborhood F constraint} x2 + x5 + x7 ≥ 1 {Neighborhood G constraint} x1 + x4 + x6 ≥ 1 {Neighborhood H constraint} x1 + x6 + x8 ≥ 1 {Neighborhood I constraint} x1 + x2 + x7 ≥ 1 {Neighborhood J constraint} Which of the constraints is a set covering constraint? (A set covering constraint in this case makes sure that certain neighborhood(s) is(are) will have at least a location within 15 minutes of them) Group of answer choices: All of the choices are correct. Neighborhood F constraint Neighborhood C constraint Neighborhood A constraint
A new pizza restaurant is moving into town. The owner is considering a number of potential sites and would like to minimize the initial investment involved with purchasing locations. However, the owner is very concerned about delivery time and wants to make sure that every neighborhood in the city can have a pizza delivered in 15 minutes or less. The owner has divided the city into 10 neighborhoods (A–J) and is currently considering a total of 8 different locations. To help with the decision, the owner formulated the following linear programming model:
Min 100x1 + 120x2 + 90x3 + 135x4 +75x5 + 85x6 + 110x7 + 135x8
s.t.x1 + x2 + x5 + x7 ≥ 1 {Neighborhood A constraint}
x1 + x2 + x3 ≥ 1 {Neighborhood B constraint}
x5 + x6 + x8 ≥ 1 {Neighborhood C constraint}
x1 + x4 + x7 ≥ 1 {Neighborhood D constraint}
x2 + x3 + x7 ≥ 1 {Neighborhood E constraint}
x3 + x4 + x8 ≥ 1 {Neighborhood F constraint}
x2 + x5 + x7 ≥ 1 {Neighborhood G constraint}
x1 + x4 + x6 ≥ 1 {Neighborhood H constraint}
x1 + x6 + x8 ≥ 1 {Neighborhood I constraint}
x1 + x2 + x7 ≥ 1 {Neighborhood J constraint}
Which of the constraints is a set covering constraint? (A set covering constraint in this case makes sure that certain neighborhood(s) is(are) will have at least a location within 15 minutes of them)
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