A $16\mathrm{.}48-km-$long regional rail line from center city to suburb has the following characteristics during the afternoon peak hour. In addition, the line has the following stations, station spacing, and boarding and alighting:

$\backslash$table$[[$Station$,$A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I$],[\backslash$table$[[$Boarding$],[($prs$/$h$)]],2640,1968,3156,288,160,20,48,12,0],[\backslash$table$[[$Alighting$],[($prs$/$h$)]],0,96,144,1032,1240,3020,1032,528,1200]]$

Train consists are $5$ cars, and each car has $94$ seats and a total capacity of $145$ spaces.

Operating speed on the line is $42k\frac{m}{h}.$ Terminal times cannot be shorter than $5$min at each end.

a$.$ Compute and draw the load diagram $($profile of passengers, offered seated, and total capacities$).$ Compute and show the MLS$.$

b$.$ Compute schedule I for the line adopting the maximum load factor $=0\mathrm{.}65$ on the MLS$.$

c$.$ Compute two other schedules for a more economical operation when alternative trains would turn back at station $F$ and at terminal I: schedule II would again have load factor $=0\mathrm{.}65,$ while schedule III should be based on a higher load factor $=0\mathrm{.}87.$

d$.$ Compare the three schedules by:

The number of trains and cars required

Work utilization coefficients