a. If Montreal wants to pursue the objective of minimizing the distance the snow must be moved (and therefore the cost of removing snow), how much snow should it plan to move from each sector to each disposal site?

b. If it costs $35 to move 1000 cubic meters of snow one kilometer, how much should Montreal plan on spending on the transportation for the removal of snow?

c. If Montreal wants to pursue the objective of maximizing the amount of contaminant that is removed from transported snow, how much snow should it plan to move from each sector to each disposal site and what transportation cost is associated with this solution?

d. Suppose Montreal wants to minimize the maximum percentage deviation from the optimal value for each of the two objectives mentioned earlier. What is the optimal solution and how far is each objective function from its optimal value?

e. Suppose the removal of contaminants is regarded as five times more important than transportation cost minimization. What solution minimizes the maximum weighted percentage deviation for each objective? How far is each objective from its optimal value?

f. What other suggestions might you have for Montreal as it attempts to deal with these two conflicting objectives?

Snow removal and disposal are important and expensive activities in Montreal and many 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 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 the physical size of the disposal facility. The annual capacities for five different snow disposal sites are given below (in 1,000s of cubic meters).

The snow transported to various disposal sites often is contaminated by salt and deicing 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 below. The amount of contaminant contained in removed snow is relatively constant across sectors.

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 between 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 ten sectors in the city.

Using historical snowfall data, the city can estimate the annual volume of snow requiring removal in each sector as four times the length of streets in the sectors in meters (i.e., it is assumed that 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 1000s of cubic meters) for each sector in the comingyear.

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Disposal Site 2 3 4 Capacity 30250 500 400 200 Disposal Site 3 20% 2 4 5 Contaminant Removed 30% 40% 70% 50% 3869817923 9888865478 414297265 7998776776 3- 9375 159261 4834269567 4196192 15 1223346646 |4| 4 4 6 5 2 8 4 12 1|3212144533 1234567890