A New Pizza Restaurant Is Moving into Town $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if location } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$

question 70

Multiple Choice

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 +75x 5 + 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} $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if location } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$
Which of the locations is within 15 minutes of neighborhoods C, H, and I?

• A) Location 2
• B) Location 4
• C) Location 6
• D) Location 8
• E) None of these locations is within 15 minutes of neighborhoods C, H, and I.

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Definitions:

Ultimatum Game

A game in experimental economics where two players decide on how to divide a sum of money; one proposes the split, and the other can accept or reject it.

Behavioral Economists

Researchers who study the effects of psychological, cognitive, emotional, cultural, and social factors on the economic decisions of individuals and institutions.

Dictator Game

An experimental game in economics and psychology where one player, the "dictator," determines how to split an endowment between themselves and another player.

Ultimatum Game

A game in economic experiments where one party offers how to divide a sum of money with another party, who can accept or reject the offer.