A City Wants to Locate 2 New Fire Fighting Ladder $\quad$

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.
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\underline{\text { To zone }}$
$\begin{array}{l}\begin{array} { c c c c c c } \text { No. tall building } & \text { From zone } & 1 & 2 & 3 & 4 \\\hline 50 & 1 & 0 & 2 & 1 & 6 \\90 & 2 & 2 & 0 & 4 & 5 \\60 & 3 & 1 & 4 & 0 & 1 \\70 & 4 & 6 & 5 & 1 & 0\end{array}\end{array}$
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
$$\begin{array} { c l c } \text { Zone } & \text { Covers these zones } & \text { With this many buldings} \\\hline 1 & 1,2,3 & 200 \\2 & 1,2 & 140 \\3 & 1,3,4 & 180 \\4 & 3,4 & 130\end{array}$$ $\text { MAX: } \quad 200 \mathrm{X}_{1+}+140 \mathrm{X}_{2}+180 \mathrm{X}_{3}+130 \mathrm{X}_{4}$

$\begin{array}{ll}\text { Subject to: } & \mathrm{X}_{1}+\mathrm{X}_{2}+\mathrm{X}_{3}+\mathrm{X}_{4}=2 \\& \mathrm{X}_{1}+\mathrm{X}_{2} \leq 1 \\& \mathrm{X}_{\mathrm{i}}=0,1\end{array}$