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 26

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 within 5 minutes of the science, music, math, and business buildings?

• A) Location 2
• B) Location 4
• C) Location 5
• D) Location 6
• E) None of these locations is within 5 minutes of the listed buildings.

---

Definitions:

Truth Values

The validity status of a statement, which can be either true or false in classical logic.

Truth Table

A mathematical table used in logic to compute the truth values of logical expressions based on their truth values of their components.

Atomic Sentences

Simple sentences that contain no logical connectives or only one predicate that asserts something about a subject.

Short Form Truth Table

A method used in logical analysis to determine the validity of logical statements by systematically examining all possible truth values of its components in a concise format.