Nova Company$$s total overhead cost at various levels of activity are presented below:

Month Machine$-$Hours Total Overhead Cost

April $53,000$ $ $205,830$

May $43,000$ $ $181,730$

June $63,000$ $ $229,930$

July $73,000$ $ $254,030$

Assume the total overhead cost above consists of utilities, supervisory salaries, and maintenance. The breakdown of these costs at the $43,000$ machine$-$hour level of activity is:

Utilities $($variable$)$ $ $51,600$

Supervisory salaries $($fixed$)65,000$

Maintenance $($mixed$)65,130$

Total overhead cost $ $181,730$

Nova Company$$s management wants to break down the maintenance cost into its variable and fixed cost elements.

Required:

Estimate how much of the $$254,030$ of overhead cost in July was maintenance cost. $($Hint: To do this, it may be helpful to first determine how much of the $$254,030$ consisted of utilities and supervisory salaries. Think about the behavior of variable and fixed costs.$)$

Using the high$-$low method, estimate a cost formula for maintenance in the form Y $=$ a $+$ bX$.$

Express the company$$s total overhead cost in the form Y $=$ a $+$ bX$.$

Estimate how much of the $$254,030$ of overhead cost in July was maintenance cost. $($Hint: to do this, it may be helpful to first determine how much of the $$254,030$ consisted of utilities and supervisory salaries. Think about the behavior of variable and fixed costs.$)$