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

Month, Machine$-$Hours, Total Overhead Cost

April, $51,000,$ $$206,330$

May, $41,000,$ $$179,030$

June, $61,000,$ $$233,630$

July, $71,000,$ $$260,930$

Assume the total overhead cost above consists of utilities, supervisory salaries, and maintenance. The breakdown of these costs at the $41,000$ machine$-$hour level of activity is:

Utilities $($variable$)$ $ $61,500$

Supervisory salaries $($fixed$)51,000$

Maintenance $($mixed$)66,530$

Total overhead cost $ $179,030$

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

Required:

Estimate how much of the $$260,930$ of overhead cost in July was maintenance cost. $($Hint: To do this, it may be helpful to first determine how much of the $$260,930$ 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$.$

What total overhead cost would you expect at an activity level of $46,000$ machine$-$hours?