A $30-$station transfer line has an ideal cycle time of $0\mathrm{.}75$ min, an average downtime of $6\mathrm{.}0$ min per line stop occurrence, and a station failure frequency of $0\mathrm{.}01$ for all stations. A proposal has been submitted to locate a storage buffer. Case $1)$ The proposal is to divide the line into three stages, that is$,$ with two storage buffers located between stations $10$ and $11,$ and between stations $20$ and $21,$ respectively. Case $2)$ The proposal is to use an asynchronous line with large storage buffers between every pair of stations on the line; that is a total of $29$ storage buffers.

For each case, determine $($a$)$ the current line efficiency and production rate, and $($b$)$ the

maximum possible line efficiency and production rate that would result from installing the

storage buffer.