The Hartnett Corporation manufactures baseball bats with Pudge Rodriguez's autograph stamped on them. Each bat sells for

$$35$ and has a variable cost of $$22.$ There are $$97,500$ in fixed costs involved in the production process.

a$.$ Compute the break$-$even point in units.

b$.$ Find the sales $($in units$)$ needed to earn a profit of $$262,500.$