Q$1$ Waste Collection Problem

To allow timely collection and processing of waste in recycling operations, a city is divided up into

several sectors$,$ and waste collection operations are carried out concurrently in each sector.

Accumulated waste is loaded onto trucks and hauled away to waste disposal sites. Due to

contractual reasons, each sector may be assigned to only a single disposal site; however, each

disposal site may receive waste from multiple sectors$.$ The different types of disposal sites can

accommodate different amounts of waste due to the physical size of the disposal facility. The

annual capacities for three different waste disposal sites are given in the following table $($in $1,000$s

of cubic meters$).$

Table $1$: Capacities of the disposal sites $($in $1,000$ cubic meters$)$

The cost of disposing of waste depends mainly on the distance it must be transported, and it costs

$$100$ to transport $1,000$ cubic meters of waste $1$ kilometer. The following table summarizes the

distances $($in kilometers$)$ for $6$ sectors in the city.

Table $2$: Distances $($in $km\text{'}$s$)$ between sectors and disposal cites

Using historical waste data, the planners estimate the annual volume of waste in these sectors

for the upcoming year, given in the following table $($in $1,000$ s of cubic meters$).$

Table $3$: Amount of waste in each sector $($in $1,000$ cubic meters$)$