Trace Ltd produces chemical X$,$ used in the manufacturing of a pesticide by mixing and heating three ingredient: A$1,$B$2$ and C$3.$The company uses a standard costing system to monitor its costs.

The standard material cost for $100$kg of Chemical X is as follow:

Input kg Cost per kg$($K$)$ Cost per $100$kg of component X $($K$)$

A$14010\mathrm{.}00400\mathrm{.}00$

B$26025\mathrm{.}001,500\mathrm{.}00$

C$3205\mathrm{.}00100\mathrm{.}00$

Total $1202,000\mathrm{.}00$

Notes:

$>$ The mixing and heating process is subject to a standard evaporation loss.

$>$ A$1,$B$2$ and C$3$ are agricultural product and their quality and price varies significantly from year to year.

Standard prices are set at the average market price over the last five years. Trace Ltd has purchasing manager who is responsible for pricing and supplier contracts.

$>$ The standard mix is set by the finance department. The last time this was done was at the product launch which was five years ago. It has not changed since last month $2,300$kg of Chemical X was produced, using the following inputs:

Input Kg Cost per Kg $($K$)$ cost per $100$kg of Chemical X $($K$)$

A$11,1009\mathrm{.}009,900\mathrm{.}00$

B$21,25030\mathrm{.}0037,500\mathrm{.}00$

C$34605\mathrm{.}002,300\mathrm{.}00$

Total $281049,700\mathrm{.}00$

At the end of each month, the production manager receives a standard cost operating statement from Trace Ltd$\text{'}$s performance manager. The statement contains material price and usage variances, labour rate and efficiency variances, and overhead expenditure and efficiency variances for the previous month. No commentary on the variances is given and the production manager receives on other feedback on the efficiency of the Chemical X process.

Required:

$($i$)$ Explain a standard and four $(4)$ types of standards in costing.

Calculate the following variance for the last month:

$($i$)$ material usage variance for each ingredient and in total.

$($ii$)$ total material mix variance.

$($iii$)$ total material yield variance.