The standard material cost for production of $100$ Kgs of Chemical D is made up of:

Chemical A $30$ Kgs @ P$4\mathrm{.}00$ per Kg

Chemical B $40$Kgs @ P$5\mathrm{.}00$ per Kg

Chemical C $80$Kgs @P$6\mathrm{.}00$ per Kg

In a batch, $500$Kgs of Chemical D was produced from a mix of:

Chemical A $140$ Kgs @ a cost of P$588$

Chemical B $220$ Kgs @ a cost of P$1056$

Chemical C $440$Kgs @ a cost of P$2860$

Required: Calculate the following variances:

$($a$)$ Material cost variance. $(4$ marks$)$

$($b$)$ Material price variance. $(4$ marks$)$

$($c$)$ Material usage variance $(4$ marks$)$

$($d$)$ Material mix variance. $(4$ marks$)$

$($e$)$ Material yield variance. $(4$ marks$)$