Problem $1$

A start$-$up company, Macrotech, plans to produce a device to translate Morse code to a written message on a home computer and to send written messages in Morse code over the airwaves. The device is primarily of interest to ham radio enthusiasts. The president, Ron Lodel, estimates that it would require a $$30,000$ initial investment. Each unit costs him $$20$ to produce and each sells for $$85.$

$($a$)$ How many units must be sold in order for the firm to recover its initial investment?

$($b$)$ What is the total revenue at the break$-$even volume?