Santucci Appliances received an invoice dated August $11$ with terms $2/10$ E$.$O$.$M$.$ for the items listed below.

$5$ refrigerators at $$950$ each less $30\%$ and $5\%$

$3$ dishwashers at $$743$ each less $15\frac{2}{3}\%,12\mathrm{.}8\%,$ and $3\%$

$($a$)$ What is the last day for taking the cash discount?

$($b$)$ What is the amount due if the invoice is paid on the last day for taking the discount?

$($c$)$ What is the amount of the cash discount if a partial payment is made such that a balance of $$1700$ remains outstanding on the invoice?