Markland Manufacturing intends to increase capac$-$ ity by overcoming a bottleneck operation by adding new equip$-$ ment. Two vendors have presented proposals. The fixed costs for proposal A are $$50,000,$ and for proposal B$,$ $$70,000.$ The variable cost for A is $$12\mathrm{.}00,$ and for B$,$ $$10\mathrm{.}00.$ The revenue generated by each unit is $$20\mathrm{.}00.$

a$)$ What is the break$-$even point in units for proposal A$?$

b$)$ What is the break$-$even point in units for proposal B$?$