On $30$ April $2017,$ you were hired as a management accountant for Foxworthy Manufacturing. Kim Foxworthy, the plant manager, has expressed frustration at the company's inability to accurately forecast total factory overhead using the following formula:

Total factory overhead costs $=$ R$20000+$ R$9$X

R$2=0\mathrm{.}3$

Where X $=$ Direct labour hours

The following printout was generated by the data processing department using observations gathered during the past $12$ months:

Intercept $48000$

Regression coefficients:

Units $34$

Setups $12$

Engineering hours $5$

R$20\mathrm{.}96$

Budgeted activity levels for April:

Units $10000$

Setups $200$

Engineering hours $50$

Direct labour hours $20000$

Required:

Provide the following for Kim Foxworthy:

$4\mathrm{.}1$ A new cost formula for estimating factory overhead costs. $(5)$

$4\mathrm{.}2$ An example of how the formula can be used to estimate costs for the month of April. $(2)$

$4\mathrm{.}3$ An explanation as to why the previous formula failed to accurately predict factory overhead costs. $(3)$