Q$.1$ The from$-$to chart below indicates the number of loads moved per $8-$hr day $($above the slash$)$ and the distances in ft $($below the slash$)$ between departments in a particular factory. Fork lift trucks are used to transport the materials. They move at an average speed $\backslash (=275\backslash )\backslash (\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$min$\}\backslash )($loaded$)$ and $\backslash (350\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$min$\}\backslash )($empty$).$ Load handling time $($loading plus unloading$)$ per delivery is $1\mathrm{.}5$ min $,$ and anticipated traffic factor $\backslash (=0\mathrm{.}9\backslash ).$ Availability $\backslash (=95\backslash \%\backslash )$ and worker efficiency $\backslash (=110\backslash \%\backslash ).$ Determine the number of trucks required under each of the following assumptions: $($a$)$ the trucks never travel empty; and $($b$)$ the trucks travel empty a distance equal to their loaded distance.