Production rate for an assembled product $=47\mathrm{.}5$ units per hour. Total work content time $=32$ minutes of direct manual labor. The line operates at $95\%$ uptime. Ten workstations have two workers on opposite sides of the line so that both sides of the product can be worked on simultaneously. The remaining stations have one worker. Repositioning time lost by each worker is $0\mathrm{.}2$ min$/$cycle$.$ It is known that the number of workers on the line is two more than the number required for perfect balance. Determine $($a$)$ number of workers, $($b$)$ number of workstations, $($c$)$ balancing efficiency, and $($d$)$ average manning level.