A City Wants to Locate 2 New Fire Fighting Ladder

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