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A Cellular Phone Company Wants to Locate Two New Communications

Question 60

Essay

A cellular phone company wants to locate two new communications towers to cover 4 regions.The company wants to minimize the cost of installing the two towers.The regions that can be covered by each tower site are indicated by a 1 in the following table:
Tower Sites
 Region 1234 A 11 B 111 C 111 D 11 COST $000 s) 200150190250\begin{array}{rrrrr}\text { Region } & 1 & 2 & 3 & 4 \\\hline \text { A } & & 1 & & 1 \\\text { B } & 1 & & 1 & 1 \\\text { C } & 1 & 1 & 1 &\\\text { D } & 1 & & & 1 \\\hline \text { COST } \$ 000 \text { s) } & 200 & 150 & 190 & 250\end{array}
MIN: 200 X1 + 150 X2 + 190 X3 + 250 X4
Subject to: X2 + X4 ? 1
X1 + X3 + X4 ? 1 X1 + X2 + X3 ? 1 X1 + X4 ? 1
X1 + X2 + X3 + X4 = 2 Xi = 0,1
Based on this ILP formulation of the problem what formulas should go in cells F6:F14 of the following Excel spreadsheet?
 A cellular phone company wants to locate two new communications towers to cover 4 regions.The company wants to minimize the cost of installing the two towers.The regions that can be covered by each tower site are indicated by a 1 in the following table: Tower Sites   \begin{array}{rrrrr} \text { Region } & 1 & 2 & 3 & 4 \\ \hline \text { A } & & 1 & & 1 \\ \text { B } & 1 & & 1 & 1 \\ \text { C } & 1 & 1 & 1 &\\ \text { D } & 1 & & & 1 \\ \hline \text { COST } \$ 000 \text { s) } & 200 & 150 & 190 & 250 \end{array}   MIN: <sup>200 X</sup><sub>1 </sub><sup>+ 150 X</sup><sub>2 </sub><sup>+ 190 X</sup><sub>3 </sub><sup>+ 250 X</sup><sub>4</sub> Subject to: <sup>X</sup><sub>2 </sub><sup>+ X</sup><sub>4 </sub><sup>? 1</sup> X<sub>1 </sub>+ X<sub>3 </sub>+ X<sub>4 </sub>? 1 X<sub>1 </sub>+ X<sub>2 </sub>+ X<sub>3 </sub>? 1 X<sub>1 </sub>+ X<sub>4 </sub>? 1 X<sub>1 </sub>+ X<sub>2 </sub>+ X<sub>3 </sub>+ X<sub>4 </sub>= 2 X<sub>i </sub>= 0,1 Based on this ILP formulation of the problem what formulas should go in cells F6:F14 of the following Excel spreadsheet?

Correct Answer:

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\[\begin{array}{l}
\begin{array} { l l }...

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