A producer of inkjet printers is planning to add a new line of printers, and you have been asked to balance the process, given the following task times and precedence relationships. Assume that cycle time is to be the minimum possible. a$.$ Do each of the following: $(1)$ Enter the number of following tasks for each of the tasks shown in the table below. $/$r$/$n $(2)$ Assign tasks to stations in order of greatest number of following tasks. Use greatest positional weight as a tiebreaker rule $/$r$/$n $(3)$ Determine the percentage of idle time. $($Round your answer to $2$ decimal places. Omit the $"\backslash \%"$ sign in your response.$)$ Percentage of idle time $\backslash (\backslash \%\backslash )(4)$ Compute the rate of output in printers per day that could be expected for this line assuming a $420-$minute working day. $($Round your answer $2$ decimal places.$)$ Rate of output units per day b$.$ Answer these questions: $(1)$ What is the shortest cycle time that will permit use of only two workstations? $($Round your answer to $1$ decimal place.$)$ Shortest cycle time minutes $(2)$ Determine the percentage of idle time that would result if two stations were used and each station was loaded with the worktime shown in Part b$(1).($Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Omit the $"\backslash \%"$ sign in your response.$)$ Percentage of idle time $*\backslash (\backslash \%\backslash )/$r$/$n b$.$ Answer these questions: $(1)$ What is the shortest cycle time that will permit use of only two workstations? $($Round your answer to $1$ decimal place.$)$ Shortest cycle time $*$ minutes $(2)$ Determine the percentage of idle time that would result if two stations were used and each station was loaded with the worktime shown in Part b$(1).($Leave no cells blank $-$ be certain to enter $"0"$ wherever required. Omit the $"\backslash \%"$ sign in your response.$)$ Percentage of idle time $\backslash (\backslash \%\backslash )(3)$ What is the daily output under this arrangement a using the cycle time from Part b$(1)?($Round your answer to $2$ decimal places.$)$ Daily output $*$ units per day $(4)$ Determine the output rate that would be associated with using the maximum cycle time. $($Round your answer to $2$ decimal places. Rate of output units per day