$1)$ Mandy$$s Manufacturing produces a single product that sells for $$50.$ Variable costs per unit equal $$32.$ The company estimates that fixed costs are $$64,000.$

a$)$ What is Mandy$$s breakeven point in units?

b$)$ Suppose that Mandy wants an after$-$tax profit of $$30,000.$ How many units must she sell if her tax rate is $35\%?$

c$)$ Which number is larger, your answer to a$)$ or to b$)?$ Why does this make sense?