A rail$-$guided vehicle system is being planned as part of an assembly cell consisting of two

parallel lines, as in Figure P$10\mathrm{.}9.$ In operation, a base part is loaded at station $1$ and delivered

to either station $2$ or $4,$ where components are added to the base part. The RGV then goes to

either station $3$ or $5,$ respectively, where further assembly of components is accomplished.

From stations $3$ or $5,$ the completed product moves to station $6$ for removal from the system.

Vehicles remain with the products as they move through the station sequence; thus, there is

no loading and unloading of parts at stations $2,3,4,$ and $5.$ After unloading parts at station $6,$

the vehicles then travel empty back to station $1$ for reloading. The hourly moves $($parts$/$hr$,$

above the slash$)$ and distances $($ft$,$ below the slash$)$ are listed in the table below. Moves

indicated by $"$L$"$ are trips in which the vehicle is loaded, while $"$ E $"$ indicates moves in which

the vehicle is empty. RGV speed $=150$ft$//$min$.$ Assembly cycle times at stations $2$ and $3=$

$4\mathrm{.}0$ min each, and at stations $4$ and $5=6\mathrm{.}0$min each. Load and unload times at stations $1$ and

$6$ respectively are each $0\mathrm{.}75$ min $.$ Traffic factor $=1\mathrm{.}0$ and availability $=1\mathrm{.}0.$ How many

vehicles are required to operate the system? Give Answer with Flexible manufacturing formula