$3\mathrm{.}1(15$ points$)$ A batch of parts is produced on a semi$-$automated production machine in a sequential batch production operation. Batch quantity is $300$ units. Setup takes $55$min. A worker loads and unloads the machine each cycle, which takes $0\mathrm{.}75$min. Machine processing time is $3\mathrm{.}46mi\frac{n}{c}$ycle, and tool handling time is negligible. One part is produced each cycle. Determine $($a$)$ average cycle time, $($b$)$ time to complete the batch, and $($c$)$ average production rate.