Consider a two$-$station production line in which no inventory is allowed between stations $($i$.$e$.,$ the stations are tightly coupled$).$ Station $1$ consists of a single machine that has potential daily production of one, two, three, four, five, or six units, each outcome being equally likely $($i$.$e$.,$ potential production is determined by the roll of a single die$).$ Station $2$ consists of a single machine that has potential daily production of either three or four units, both of which are equally likely $($i$.$e$.,$ it produces three units if a fair coin comes up heads and four units if it comes up tails$).$

Compute the capacity of each station $($i$.$e$.,$ in units per day$).$ Is the line balanced $($i$.$e$.,$ do both stations have the same capacity$)?$