The University Administration Would Like to Add Some Additional Parking $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if location } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$

question 10

Multiple Choice

The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces) . The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10) . To help with the decision, the management science department formulated the following linear programming model:
Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6
s.t. x1 + x2 + x5 + x6 ? 1 {Residence Hall A constraint}
X1 + x2 + x3 ? 1 {Residence Hall B constraint}
X4 + x5 + x6 ? 1 {Science building constraint}
X1 + x4 + x5 ? 1 {Music building constraint}
X2 + x3 + x4 ? 1 {Math building constraint}
X3 + x4 + x5 ? 1 {Business building constraint}
X2 + x5 + x6 ? 1 {Auditorium constraint}
X1 + x4 + x6 ? 1 {Arena constraint}
X1 + x2 + x3 + x4 + x5 + x6 ? 4 {Total locations 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 the most expensive?

• A) Location 2
• B) Location 3
• C) Location 4
• D) Location 5
• E) Location 6

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Definitions:

Leverage

In statistics, the influence a single data point has on the overall outcome of a regression analysis.

Linear Model

A statistical approach for modeling the relationship between a scalar response and one or more explanatory variables using straight-line equations.

Labeled Points

Points in a space marked with identifiers or symbols to denote specific positions or values.

Data

Factual information used as a basis for reasoning, discussion, or calculation, often numeric in form.