Consider the layout shown in Figure, and the From$-$To Chart presented in Table. The AGVS includes load station $1$ where raw parts enter the system for delivery to any of three production stations $2,3,$ and $4.$ Unload station $5$ receives finished parts from the production stations. Load and unload times at stations $1$ and $5$ are each $0\mathrm{.}25$ min $.$ Production rates for each workstation are indicated by the delivery requirements in Table. Some parts must be transshipped between stations $2$ and $4.$ Vehicles move in the direction indicated by the arrows in the figure. The AGVs travel at a speed of $0\mathrm{.}5\frac{m}{sec},$ and the traffic factor $=0\mathrm{.}9.$ Assume reliability $=0\mathrm{.}95\%.$

i$)$ If the vehicles operate according to the following scheduling rules: $($a$)$ vehicles delivering raw work parts from station $1$ to stations $2,3,$ and $4$ must return empty to station $5$; and $($b$)$ vehicles picking up finished parts at stations $2,3,$ and $4$ for delivery to station $5$ must travel empty from station $1,$ then how many automated guided vehicles will be required to operate the system.

$[12$ Marks$]$

ii$)$ If vehicles delivering raw work parts from station $1$ to stations $2,3,$ and $4$ must pick up finished parts at these respective stations for delivery to station $5,$ then how many automated guided vehicles will be required to operate the system.

$[8$ Marks$]$

$\backslash$table$[[$To$,1,2,3,4,5$