ProTest Company is in the biochem industry and manufactures only a single product, a sophisticated testing equipment for chronic illnesses and diseases with the name Test$-$K$.$ The following standard costs apply:

For the period, production was budgeted at $15,000$ units.

Direct materials $2\mathrm{.}5$ kilos at $$9$ per kilo

Direct labour $4\mathrm{.}5$ hours at $$13\mathrm{.}50$ per hour

Budgeted fixed production overheads $$405,000$

Fixed production overheads are absorbed on the basis of standard direct labour hours.

The actual data for the period, when production was $15,900$ units, are as follows:

Direct materials purchased and used $41,250$ kilos costing $$8\mathrm{.}70$ per kilo

Direct labour $69,900$ hours at a cost of $$13\mathrm{.}95$ per hour

Fixed production overheads $$425,000$

Required:

a$)$ Calculate the following production cost variances for the period:

$($i$)$ direct material total

$($ii$)$ direct material price

$($iii$)$ direct material usage

$($iv$)$ direct labour total

$($v$)$ direct labour rate

$($vi$)$ direct labour efficiency

$($vii$)$ fixed production overhead expenditure

$($viii$)$ fixed production overhead volume.

b$)$ Provide specific reasons for the variances on each of the calculations done above for:

i$.$ Direct material price

ii$.$ Direct material usage

iii. Direct labour rate

iv$.$ Direct labour efficiency

You are required to state whether it is a favorable or adverse variance.

c$)$ Discuss several ways in which standard$-$costing systems should be adapted in today$$s manufacturing environment.