Question $3$: $(10$ pts$)$

Suppose a system throughtput is $300$ storage and retreivals per hour. The AS$/$RS has $10$ gisles and each is served by one S$/$R machine. Furthermore, $30\%$ of the operations are performed as $($single commands and the rest as dual command operations. The aisle length $($rack length$)$ is $275ft$ and aisto height is $77\mathrm{.}5f.$ The horizontal and vertical speeds are $300\frac{f}{m}in$ and $70\frac{f}{m}in,$ respectively. A PID operation of the SIR nachine takes approximately $0\mathrm{.}35$min.

a$.$ Determine the percent utilization of the machine.