As part of a major plant renovation project, the industrial engineering department has been asked to balance a revised assembly line to achieve an output rate of $240$ units per eight$-$hour day. Task times and precedence relationships are as follows:

Task Duration $($minutes$)$ Precedes Task

a $0\mathrm{.}2$ b

b $0\mathrm{.}4$ d

c $0\mathrm{.}2$ d

d $0\mathrm{.}4$ g

e $1\mathrm{.}2$ f

f $1\mathrm{.}2$ g

g $1\mathrm{.}0$

Do each of the following:

a$.$ This part of the question is not part of your Connect assignment.

b$.$ Determine the required cycle time.

Cycle time $0\mathrm{.}25$ Numeric ResponseEdit Unavailable. $0\mathrm{.}25$ incorrect. minutes per unit

c$.$ Determine the minimum number of workstations needed. $($Round the final answer to next whole number.$)$

Number of workstations $35$ Numeric ResponseEdit Unavailable. $35$ incorrect.

d$.$ Assign the tasks to workstations using the heuristic rule $$Assign the task with the most followers.$$ Use the heuristic rule $$Assign the task with the longest time$$ as a tiebreaker. If a tie still exists, choose randomly. $($Do not leave any empty spaces; input a $0$ wherever it is required. Round the final answers to $1$ decimal place.$)$

Workstation Task Idle time

$1$

$2$

$3$

e$.$ Calculate the percentage idle time for the assignments in part d$.($Round the final answer to $2$ decimal places.$)$

Percentage Idle time $\%$