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 74

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.
Min 200x1 + 250x2 + 225x3 + 190x4 +215x 5 + 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 is the least expensive?

• A) Crew 1
• B) Crew 2
• C) Crew 3
• D) Crew 4
• E) Crew 5

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Definitions:

Sympathetic Nervous System

A part of the autonomic nervous system that orchestrates the body's rapid involuntary response to dangerous or stressful situations.

Parasympathetic Nervous System

Part of the autonomic nervous system responsible for rest and digestion, counterbalancing the sympathetic nervous system.

Bowel

The part of the digestive system that extends from the stomach to the anus, including the small and large intestines, responsible for nutrient absorption and waste elimination.

Bladder

An organ in the body that collects urine excreted by the kidneys before disposal by urination.