A City Wants to Locate 2 New Fire Fighting Ladder

question 44

Essay

A city wants to locate 2 new fire fighting ladder trucks to maximize the number of tall buildings which they can cover within a 3 minute response time.The city is divided into 4 zones.The fire chief wants to locate no more than one of the trucks in either Zone 1 or Zone 2.The number of tall buildings in each zone and the travel time between zones is listed below.
$$\begin{array}{c}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { To zone }\\\begin{array} { c c c c c c } \text { No. tall buildings } & \text { Fram zone } & 1 & 2 & 3 & 4 \\\hline 50 & 1 & 0 & 2 & 1 & 6 \\90 & 2 & 2 & 0 & 4 & 5 \\60 & 3 & 1 & 4 & 0 & 1 \\70 & 4 & 6 & 5 & 1 & 0\end{array}\end{array}$$
Based on this ILP formulation of the problem what values should go in cells B5:G24 of the following Excel spreadsheet?
Let X_i = 1 if truck located in zone i,0 otherwise
$$\begin{array} { c c c } \text { Zone } & \text { Covers these zones } & \text { With the many building } \\\hline 1 & 1,2,3 & 200 \\2 & 1,2 & 140 \\3 & 1,3,4 & 180 \\4 & 3,4 & 130\end{array}$$
MAX: ^{200 X}₁ ^{+ 140 X}₂ ^{+ 180 X}₃ ^{+ 130 X}₄
Subject to: ^X₁ ^{+ X}₂ ^{+ X}₃ ^{+ X}₄ ^{= 2}
X₁ + X₂ ? 1
X_i = 0,1

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Definitions:

Reaction Time

The amount of time it takes to respond to a stimulus.

Observable Behaviours

Observable and quantifiable behaviors or responses of a person to either external or internal factors.

Psychological Perspective

A viewpoint in psychology that emphasizes understanding human behavior by examining mental functions and processes.

Emotional Reactions

Responses characterized by intense feelings that occur in reaction to an external stimulus or internal thought process.