Acme Company purchases raw material $x(RMx)$ at a cost of $$8\mathrm{.}40$ per gallon. Acme can resell RMX as is for $$9\mathrm{.}00$ per gallon or it can further process $RMx$ to make Product $Z.$ It takes $0\mathrm{.}80$ gallons of RMX to make one unit of Product $Z,$ which Acme can sell for $$13\mathrm{.}20$ per unit. In addition to the cost of RMX$,$ Acme incurs $$3\mathrm{.}30$ of additional variable costs to make and sell one unit of Product $Z.$ The monthly traceable fixed costs related to Product $Z$ include $$11,475$ of salaries paid to Product Z production and sales managers, as well as $$2,025$ of depreciation expense on specialized manufacturing equipment. The specialized equipment has no resale value. How many units of Product $Z$ does Acme need to sell each month to break$-$even on processing RMX into Product $Z$ as opposed to merely reselling RMX without further processing?

$4,250$ units