Note: This Problem Requires the Use of a Linear Programming $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if location } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$

question 60

Multiple Choice

Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver.
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} $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if location } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$
Set up the problem in Excel and find the optimal solution. Which locations are selected?

• A) Location 1
• B) Location 3
• C) Location 5
• D) None of locations 1, 3, and 5 are selected.
• E) All of locations 1, 3, and 5 are selected.

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Definitions:

Continuum

A continuous sequence or range of values or elements that vary by slight degrees without sharp distinctions.

Societal Harm

Negative impacts on society or segments of it, caused by actions or policies that lead to inequality, injustice, or environmental damage.

Social Diversions

Activities or entertainments that are pursued for pleasure and tend to draw people away from more serious social issues or engagements.

Amusement

A broad term referring to the activities, events, or experiences designed to provide enjoyment or entertainment to individuals or groups.