$24$ A worker is currently responsible for tending two machines in a certain production cell. The service time per machine is $0\mathrm{.}35$min and the time to walk between machines is $0\mathrm{.}15$min. The machine automatic cycle time is $1\mathrm{.}90$min. If the worker's hourly rate is $$\frac{12}{h}r$ and the hourly rate for each machine is $$\frac{18}{h}r,$ determine $($a$)$ the current hourly rate for the cell, and $($b$)$ the current cost per unit of product, given that two units are produced by each machine during each machine cycle. $($c$)$ What is the percentage of idle time for the worker? $($d$)$ What is the optimum number of machines that should be used in the cell, if minimum cost per unit of product is the decision criterion?