$1.$ Consider a two station production line in which no inventory is allowed $($No WIP. WIP left over after the day is discarded$).$ Station $1$ consists of a single machine that has a potential daily production of one, two, three, four, five, or six units. Each of these potential outcomes is equally likely. $($you could throw a dice and have it tell you how many nits were produced on any theoretical day.$)$ Station $2$ consists of a single machine that has potential daily production of either three or four units, both of which are equally likely. $($you could flip a coin with a $3$ on one side and a $4$ on the other side to determine the daily production on any given theoretical day.$)$

a$.$ Compute and describe the capacity of each station on average in units per day. Is the line balanced $($do each of the stations have the same average capacity?$)$

b$.$ Compute and describe the expected daily throughput of the line. Why does this differ from you answer to number $1?$

c$.$ Describe how this should impact production planning and management for this process. What strategies can be used to achieve the highest throughput?