An AS$/$RS is designed for a facility with aisles of storage with an S$/$R machine dedicated to each aisle. Each aisle is $360$ ft$.$ long and $64$ ft$.$ high. The shuttle on the S$/$R requires $20$ seconds to perform a P$/$D operation. The average horizontal speed of the S$/$R is $400$ feet per minute $($fpm$)$ and average vertical speed is $80$ fpm$.$ The horizontal and vertical movement is simultaneous. It is assumed that $40\%$ of the operations $($storage and retrieval$)$ are performed on a dual$-$command basis. Also, a peak rate of $100$ storages per hour and $100$ retrievals per hour is assumed. Calculate number of single commands and dual commands, respectively,

based on the peak rate.