$2.$ A flexible manufacturing system is being planned. It has a ladder layout as pictured in Figure $1$ and uses a rail guided vehicle system to move parts between stations in the layout. All work parts are loaded into the system at station $1,$ moved to clockwise direction one of three processing stations $(2,3,$ or $4),$ and then brought back to station $1$ for unloading. Once loaded onto its RGV$,$ each work part stays onboard the vehicle throughout its time in the FMS$.$ Load and unload times at station $1$ are each $1\mathrm{.}0$ min. Processing times per delivery at other stations are: $5\mathrm{.}0$ min at station $2,7\mathrm{.}0$ min at station $3,$ and $9\mathrm{.}0$ min at station $4.$ Hourly production of parts through the system is: $7$ parts delivery through station $2,6$ parts delivery through station $3,$ and $5$ parts delivery through station $4.$