A manufacturing company produces two types of products, A and B$.$ The variable cost per unit for product A is $$15,$ and for product B is $$20.$ The company incurs fixed costs of $$100,000.$ Product A sells for $$40$ per unit, and product B sells for $$50$ per unit.

Given that the sales mix ratio between product A and product B is $3$:$2,$

calculate: 

 

a$)$ The breakeven point in units for each product.

b$)$ The sales revenue needed to achieve a target profit of $$80,000.$