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

question 60

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
$$\begin{array} { c l c } \text { Zone } & \text { Covers these zones } & \text { With this many buldings} \\\hline 1 & 1,2,3 & 200 \\2 & 1,2 & 140 \\3 & 1,3,4 & 180 \\4 & 3,4 & 130\end{array}$$ $\text { MAX: } \quad 200 \mathrm{X}_{1+}+140 \mathrm{X}_{2}+180 \mathrm{X}_{3}+130 \mathrm{X}_{4}$

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

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Definitions:

Unadjusted Cost Of Goods Sold

The initial recording of all costs associated with the goods sold by a company before any adjustments for returns, allowances, or discounts.

Job-Order Costing

An accounting method used to track costs and evaluate the profitability of individual jobs or batches.

Work In Process

Inventory items that are in the middle of the manufacturing process and are not yet completed products.

Finished Goods

Products that have completed the manufacturing process but have not yet been sold or distributed to end-users.