$3\mathrm{.}6$ A five$-$station transfer line is being considered. All failures are expected to occur at workstations and be operation dependent. Average repair time will be $5$ cycles for each station. Average failure rates are estimated to be $0\mathrm{.}01,0\mathrm{.}02,0\mathrm{.}02,0\mathrm{.}03,$ and $0\mathrm{.}02,$ respectively.

a$.$ Compute the effectiveness of the line if no buffers are used.

b$.$ Suppose one buffer of size $10$ is to be added. Where should it be placed?

c$.$ Compute the effectiveness of the line with the buffer included.