Snow removal and disposal are important and expensive activities in Montreal and many other northern cities. Although snow can be cleared from streets and sidewalks by plowing and shoveling, in prolonged subfreezing temperatures, the resulting banks of accumulated snow can impede pedestrian and vehicular traffic and must be removed.

To allow timely removal and disposal of snow, a city is divided up into several sectors and snow removal operations are carried out concurrently in each sector. In Montreal, accumulated snow is loaded into trucks and hauled away to disposal sites $($e$.$g$.,$ rivers, quarries, sewer chutes, surface holding areas$).$ The different types of disposal sites can accommodate different amounts of snow due to physical size of the disposal facility. The annual capacities for five different snow disposal sites are given in the following table $($in $1,000$s of cubic meters$)$:

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The snow transported to various disposal sites is often contaminated by salt and de$-$icing chemicals. When the snow melts, these contaminants ultimately wind up in lakes, rivers, and the local water supply. The different disposal sites are equipped to remove different amounts of contaminants from the snow they receive. The percentage of contaminants that can be removed from the snow delivered to each disposal site is given in the following table. The amount of contaminant contained in removed snow is relatively constant across sectors$.$

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The cost of removing and disposing of snow depends mainly on the distance it must be trucked. For planning purposes, the City of Montreal uses the straight$-$line distance from the center of each sector to each of the various disposal sites as an approximation of the cost involved in transporting snow between these locations. The following table summarizes these distances $($in kilometers$)$ for $10$ sectors in the city.

$\backslash$table$[[,$Disposal Site$],[$Sector$,1,2,3,4,5,,],[1,3\mathrm{.}4,1\mathrm{.}4,4\mathrm{.}9,7\mathrm{.}4,9\mathrm{.}3,,],[2,2\mathrm{.}4,2\mathrm{.}1,8\mathrm{.}3,9\mathrm{.}1,8\mathrm{.}8,,],[3,1\mathrm{.}4,2\mathrm{.}9,3\mathrm{.}7,9\mathrm{.}4,8\mathrm{.}6,,],[4,2\mathrm{.}6,3\mathrm{.}6,4\mathrm{.}5,8\mathrm{.}2,8\mathrm{.}9,,],[5,1\mathrm{.}5,3\mathrm{.}1,2\mathrm{.}1,7\mathrm{.}9,8\mathrm{.}8,,],[6,4\mathrm{.}2,4\mathrm{.}9,6\mathrm{.}5,7\mathrm{.}7,6\mathrm{.}1,,],[7,4\mathrm{.}8,6\mathrm{.}2,9\mathrm{.}9,6\mathrm{.}2,5\mathrm{.}7,,],[8,5\mathrm{.}4,6\mathrm{.}0,5\mathrm{.}2,7\mathrm{.}6,4\mathrm{.}9,,],[9,3\mathrm{.}1,4\mathrm{.}1,6\mathrm{.}6,7\mathrm{.}5,7\mathrm{.}2,,]]$

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Removal.pdf

nowRemoval.pdf

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Using historical snowfall data, the city is able to estimate the annual volume of snow requiring removal in each sector as four times the length of streets in the sectors in meters $($that is$,$ it is assumed each linear meter of street generates $4$ cubic meters of snow to remove over an entire year$).$ The following table estimates the snow removal requirements $($in $1000$s of cubic meters$)$ for each sector in the coming year:

$\backslash$table$[[$Estimated Annual Snow Removal Requirements,,,,,,,,$],[1,2,3,4,5,6,7,8,9,10$