$2.$ Kids' Game Corporation has developed a new video game, which is to be produced on an assembly line. The production schedule requires that $360$ video games be produced in an $8-$hour day. The assembly includes $11$ tasks. The table below indicates the performance time and the sequence requirements for each task. $(1)$ What is the cycle time in seconds for this assembly operation?

$(2)$ What is the minimum number of workstations?

$(3)$ Using a precedence diagram, do assembly line balancing to group the tasks into the minimum number of workstations to minimize idle time at each station $($Use Heuristic: Number of tasks that must follow and Cycle time in $(1))$

$(4)$ What is the efficiency of the line?

$(5)$ What is the total idle time for your solution?