Audrey Inc. manufactures dolls. During $2023,$ total costs incurred in making $10,000$ dolls included $$50,000$ of fixed manufacturing overhead. The total absorption cost per doll was $$30$

$($a$.)$ Calculate the fixed manufacturing overhead cost per doll.

 $($b$.)$ Calculate the variable cost per doll.

 $($c$.)$ Express the cost of the dolls in a cost formula $($Y$=$a $+$ bx$)$

 $($d$.)$ Calculate the total cost of making $12,000$ dolls using the cost formula from $($b$.).$