Mitchell, the CEO of a manufacturing company, decided to expand the product offering of her business to include the manufacture of a specific model automotive unit. To include this product, her business would incur fixed costs of $$385,000$ per year and variable costs of $$6$ per unit. She plans to sell each unit for $$85.$

a$.$ Calculate the number of units she would have to manufacture to break even.

b$.$ While manufacturing the unit, she realized that an additional fixed cost of $$3,000$ per year was required, and also realized that to be more competitive in the market she had to drop the selling price by $20\%.$ What is the new break$-$even volume?