B$1.$ A new development residential area $($total population $52,000$ people$)$ has been proposed to accommodate the increasing population in a region. Residents are going to reside in apartment buildings. The average apartment building will be $8$ stories high and contain $12$ units $($apartments$)$ on each floor. The average unit has $2\mathrm{.}01,$ occupants, each generating an average of $1\mathrm{.}51$ kg$/$p$/$d of municipal solid waste $($MSW$).$ The apartment residents place their waste in waste chutes that carry the waste to one of the building's $2\mathrm{.}2$ m$3$ volume metal dumpsters. The waste density in these dumpsters is $220$ kg$/$m$3.$ These dumpsters are mechanically picked up by a collection truck that empties them at the apartment building and then places them back. The collection trucks have a volume of $22$ m$3$ and a compaction ratio of $2\mathrm{.}2.$

Other characteristics of the waste collection system include:

a$)$ The off$-$route factor $=0\mathrm{.}17$; b$)$ At the site time $=0\mathrm{.}15$ hours; c$)$ Assume that the time for trip from the garage to the first point and the time for the trip from the disposal facility to the garage at the end of the day is incorporated in the off$-$route factor; d$)$ Assume that the apartment buildings are serviced once a week. The collectors work $8$ hours per day; e$)$ The combined container loading and unloading time is $3$ minutes per container; f$)$ The average travel time between buildings is $0\mathrm{.}05$ hours; g$)$ The driving constants are: a$=0\mathrm{.}07$ h$/$trip and b$=0\mathrm{.}02$ h$/$km; h$)$ The average distance to the disposal site is $22$ kilometers.

B$1-5.$ Assuming $5$ days$/$week of service, how many trucks are required? B$1-1.$ How many containers are filled$/$required per building per week? B$1-2.$ What is the utilization factor for the containers $(\%$ full$)?$

B$1-3.$ What is the maximum number of containers a single truck can pick up in one trip?

B$1-4.$ If the waste is to be collected once per week, what is the maximum number of buildings a single truck service per trip?

B$1-5.$ Assuming $5$ days$/$week of service, how many trucks are required?