Scott Corp. manufactures fishing boats. During $2023,$ total costs associated with manufacturing $10,000$ boats were as follows:

Raw materials $=$ $$52,100$

Direct labor $=$ $$19,500$

Variable overhead $=$ $$8,400$

Fixed overhead $=$ $$20,000$

$($a$.)$ Calculate the cost per boat under both absorption and variable costing.

$($b$.)$ Express the cost of the boats in the cost formula $($Y$=$a $+$ bx$).$