Which of the locations is the most expensive?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 100P
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Which of the locations is the most expensive?
Multiple Choice
Location 1.
Location 4.
Location 3.
Location 5.
Location 2.
Transcribed Image Text:Which of the locations is the most expensive? Multiple Choice Location 1. Location 4. Location 3. Location 5. Location 2.
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 + 135xg
s.t. x1 + x2 + x5 + x7 2 1 {Neighborhood A constraint}
x3 2 1 (Neighborhood B constraint)
X1 + x2
X5 + X6 + x8 2 1 {Neighborhood C constraint}
x1 + x4 + x7 2 1 {Neighborhood D constraint)
x2 + x3 + x7 2 1 {Neighborhood E constraint)
x3 + x4 + x8 2 1 (Neighborhood F constraint)
x2 + x5 + x7 2 1 {Neighborhood G constraint)
x1 + x4 + x6 2 1 (Neighborhood H constraint)
x1 + x6 + x8 2 1 {Neighborhood I constraint)
x1 + x2 + x7 > 1 (Neighborhood J constraint}
1, if location j is selected
0, otherwise
Xj =
Which of the locations is the most expensive?
Transcribed Image Text: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 + 135xg s.t. x1 + x2 + x5 + x7 2 1 {Neighborhood A constraint} x3 2 1 (Neighborhood B constraint) X1 + x2 X5 + X6 + x8 2 1 {Neighborhood C constraint} x1 + x4 + x7 2 1 {Neighborhood D constraint) x2 + x3 + x7 2 1 {Neighborhood E constraint) x3 + x4 + x8 2 1 (Neighborhood F constraint) x2 + x5 + x7 2 1 {Neighborhood G constraint) x1 + x4 + x6 2 1 (Neighborhood H constraint) x1 + x6 + x8 2 1 {Neighborhood I constraint) x1 + x2 + x7 > 1 (Neighborhood J constraint} 1, if location j is selected 0, otherwise Xj = Which of the locations is the most expensive?
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