The following data pertain to the three products produced by Excellent Corporation:

The fixed costs are $$100,000$ per month.

$A{B}_{,}{C}_{?}$

Selling price per unit $$6\mathrm{.}00,$$$8\mathrm{.}00,$$$9\mathrm{.}00$

Variable costs per unit ${4\mathrm{.}50}_{,}{5\mathrm{.}50}_{,}{5\mathrm{.}50}_{?}$

Contribution margin per unit $$1\mathrm{.}50,$$$2\mathrm{.}50,$$$3\mathrm{.}50$

Contribution margin per unit

The sales mix of Excellent Corporation consists of $65\%$ of Product A$,20\%$ of Product B$,$ and $15\%$ of Product C$.$

What is the monthly break$-$even point for total units? $($Round intermediate calculations in computing average contribution margin per unit to three decimal places.$)$

$$ a$)50,000$ units

$$ b$)45,000$ units

$$ C$)180,000$ units

$$ d$)36,000$ units