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A City Wants to Locate 2 New Fire Fighting Ladder

Question 41

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.
 To zone  No. tall buildings  Fram zone 12345010216902204560314017046510\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 Xi = 1 if truck located in zone i,0 otherwise
 Zone  Covers these zones  With the many building 11,2,320021,214031,3,418043,4130\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 X1 + 140 X2 + 180 X3 + 130 X4
Subject to: X1 + X2 + X3 + X4 = 2
X1 + X2 ? 1
Xi = 0,1
 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<sub>i </sub>= 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: <sup>200 X</sup><sub>1 </sub><sup>+ 140 X</sup><sub>2 </sub><sup>+ 180 X</sup><sub>3 </sub><sup>+ 130 X</sup><sub>4</sub> Subject to: <sup>X</sup><sub>1 </sub><sup>+ X</sup><sub>2 </sub><sup>+ X</sup><sub>3 </sub><sup>+ X</sup><sub>4 </sub><sup>= 2</sup> X<sub>1 </sub>+ X<sub>2 </sub>? 1 X<sub>i </sub>= 0,1

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