Hourly delivery requirements among four departments in a factory are listed in the From$-$To table below.

Forklift trucks are used to make the deliveries. All entries in the chart are loaded transports. The deliveries

can be scheduled so there are no empty moves. All loads enter and exit the factory through Department $1.$

In the table below, the values in front of the slash indicate the number of moves per hour, and the values

following the slash represent the average distance traveled $($ft$)$ in the move. Loading time in a department

is $0\mathrm{.}40$min, and unloading time in a department is $0\mathrm{.}30$min. Average vehicle velocity is $300$ftmin,

availability is $0\mathrm{.}96,$ traffic factor is $0\mathrm{.}94,$ and operator efficiency is assumed to be $1\mathrm{.}0.$ Determine $($a$)$ travel

distances loaded and empty, $($b$)$ ideal delivery cycle time, and $($c$)$ number of vehicles required to satisfy the

delivery demand.