Question $6.(10$ points$)$ As part of a major renovation project the industrial engineering department has been asked to balance a revised assembly operation to achieve an output of $240$units per eight$-$hour working day. Task times and precedence relationships are as follows: Task a duration $0\mathrm{.}2$ minutes; Task b duration $0\mathrm{.}4$ with a as immediate predecessor; Task c duration $0\mathrm{.}2,$ immediate predecessor b; Task d duration $0\mathrm{.}4,$ no immediate predecessor; Task e duration $1\mathrm{.}2,$ immediate predecessor d; Task f duration $1\mathrm{.}2,$immediate predecessor c; Task g duration $1\mathrm{.}0,$ immediate predecessor e$,$ f$.$Based on above numbers: a$)$Determine the cycle time, the maximum cycle time, and the calculated cycle time. b$)$ Determine the number of work stations needed. c$)$ Assign tasks to workstations on the basis of greatest number of following tasks. Use longest processing time as a tiebreaker. If ties still exist, assume indifference in choice. d$)$ Compute the percentage of idle time for the assignment in part d$.$ Use the actual bottleneck cycle time in your calculation.