$.$ An assembly process involves the following ten atomic tasks with the corresponding process

times and precedence constraints:

Task Process Time $($secs$)$ Immediate

Predecessors

a $10-$

b $8-$

c $11$ a

d $7$ c$,$b

e $5$ c

f $15$ d$,$e

g $11-$

h $15$ g

i $10$ e$,$h

k $5$ f$,$i

a$.$ Using the Rank Positional Weight heuristic to design a production line for this assembly process

with a production rate of $60$ parts per hour.

b$.$ Suppose tasks a and i have to be performed at the same station since they need to share some

equipment, what is the maximum possible hourly throughput that can be obtained for this

assembly process $?$