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 65

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. What is the cost of the optimal set of locations?

• A) 210
• B) 220
• C) 265
• D) 310
• E) 435

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Definitions:

Field-Independent Style

A cognitive style where individuals tend to be more analytical and less influenced by the surrounding context in their perception and actions.

Effect Size

A quantitative measure of the magnitude of a phenomenon, typically used in statistical research to determine the strength of a particular effect.

Mental Rotation Tests

Assessments designed to measure an individual's capability to mentally manipulate two-dimensional and three-dimensional figures, a rephrased understanding of mental rotation tasks.

Engineering

the application of scientific, mathematical, and practical knowledge in order to invent, design, build, maintain, and improve structures, machines, devices, systems, materials, and processes.