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

Month Machine$-$Hours Total Overhead Cost

April $52,000$ $ $207,520$

May $42,000$ $ $183,920$

June $62,000$ $ $231,120$

July $72,000$ $ $254,720$

Assume that the total overhead cost above consists of utilities, supervisory salaries, and maintenance. The breakdown of these costs at the $42,000$ machine$-$hour level of activity is:

Utilities $($variable$)$ $ $50,400$

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

Maintenance $($mixed$)68,520$

Total overhead cost $ $183,920$

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

Required:

$1.$ Estimate how much of the $$254,720$ of overhead cost in July was maintenance cost. $($Hint: to do this, it may be helpful to first determine how much of the $$254,720$ consisted of utilities and supervisory salaries. Think about the behavior of variable and fixed costs.$)$

$2.$ Using the high$-$low method, estimate a cost formula for maintenance in the form Y $=$ a $+$ bX$.$

$3.$ Express the company$$s total overhead cost in the form Y $=$ a $+$ bX$.$

$4.$ What total overhead cost would you expect to be incurred at an activity level of $47,000$ machine$-$hours?