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

Month Machine$-$Hours Total Overhead Cost

April $51,000$ $ $202,750$

May $41,000$ $ $176,250$

June $61,000$ $ $229,250$

July $71,000$ $ $255,750$

Assume that 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$)$ $ $57,400$

Supervisory salaries $($fixed$)54,000$

Maintenance $($mixed$)64,850$

Total overhead cost $ $176,250$

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

Required:

Estimate how much of the $$255,750$ of overhead cost in July was maintenance cost. $($Hint: to do this, it may be helpful to first determine how much of the $$255,750$ 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 to be incurred at an activity level of $46,000$ machine$-$hours?