Problem $3-15$ High$$Low Method; Predicting Cost $[$LO$1,$ LO$2]$

Crosshill Company$$s total overhead costs at various levels of activity are presented below:

Month Machine$-$Hours Total Overhead Cost

April $70,000$ $ $201,600$

May $60,000$ $ $179,400$

June $80,000$ $ $223,800$

July $90,000$ $ $246,000$

Assume that the overhead cost above consists of utilities, supervisory salaries, and maintenance. The breakdown of these costs at the $60,000-$machine$-$hour level of activity in May is as follows:

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

Supervisory salaries $($fixed$)21,000$

Maintenance $($mixed$)106,800$

Total overhead cost $ $179,400$

The company wants to break down the maintenance cost into its variable and fixed cost elements.

Required:

$1.$ Estimate how much of the $$246,000$ of overhead cost in July was maintenance cost. $($Hint: To do this, first determine how much of the $$246,000$ consisted of utilities and supervisory salaries. Think about the behaviour of variable and fixed costs within the relevant range.$)($Round the "Variable cost per unit" to $2$ decimal places.$)$

$2.$ Using the high$$low method, estimate a cost formula for maintenance. $($Round the "Variable cost per unit" to $2$ decimal places.$)$

$3.$ Express the company$$s total overhead cost in the form Y $=$ a $+$ bX$.($Round the "Variable cost per unit" to $2$ decimal places.$)$

$4.$ What total overhead cost would you expect to be incurred at an activity level of $75,000$ machine$-$hours? $($Round the "Variable cost per unit" to $2$ decimal places.$)$