The University Is Scheduling Cleaning Crews for Its Ten Buildings $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if crew } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$

question 46

Multiple Choice

The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process.
Min200x1 + 250x2 + 225x3 + 190x4 +215x5 + 245x6 + 235x7 + 220x8
s.t. x1 + x2 + x5 + x7 ? 1 {Building A constraint}
X1 + x2 + x3 ? 1 {Building B constraint}
X6 + x8 ? 1 {Building C constraint}
X1 + x4 + x7 ? 1 {Building D constraint}
X2 + x7 ? 1 {Building E constraint}
X3 + x8 ? 1 {Building F constraint}
X2 + x5 + x7 ? 1 {Building G constraint}
X1 + x4 + x6 ? 1 {Building H constraint}
X1 + x6 + x8 ? 1 {Building I constraint}
X1 + x2 + x7 ? 1 {Building J constraint} $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if crew } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$
Which of the crews can be scheduled to clean building A?

• A) Crew 1
• B) Crew 2
• C) Crew 5
• D) Crew 6
• E) Crew 7

---

Definitions:

Categories

In Aristotle's philosophy, a way of classifying the world that includes ten distinct types such as substance, quantity, quality, and relation.

Mental Representations

Internal cognitive symbols, structures, or maps of the world that individuals use to understand and interact with their environment.

Subordinate-level

A specific, detailed level within a categorization hierarchy, often denoting a particular member of a larger group.

Basic-level

Refers to the most natural and preferred categorical level at which people classify and label objects, which balances specificity and generalization.