As part of a major plant renovation project, you have been asked to balance a revised assembly operation to achieve an output of $240$ units per eight$-$hour day. Task times and precedence relationships are as follows:

a $0\mathrm{.}2$ b

b $0\mathrm{.}4$ c

c $0\mathrm{.}2$ f

d $0\mathrm{.}4$ e

e $1\mathrm{.}2$ g

f $1\mathrm{.}2$ g

g $1\mathrm{.}0$ end

Do each of the following:

a$.$ Draw the precedence diagram.

b$.$ Determine the minimum cycle time, the maximum cycle time, and the actual cycle time.

c$.$ Determine the minimum number of stations needed using the actual cycle time in part b$.$

d$.$ Assign tasks to workstations on the basis of greatest number of following tasks. When there is a tie, assign the task with longest processing time first.

e$.$ Compute the percentage of idle time for the assignment in part d$.$