Bryan, the CEO of a manufacturing company, decided to expand the product offering of his business to include the manufacture of a specific model automotive unit. To include this product, his business would incur fixed costs of $$385,000$ per year and variable costs of $$5$ per unit. He plans to sell each unit for $$90.$

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

Round up to the next whole number

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