IM$19\mathrm{.}1$ Intermediate: Material usage, mix and yield variances. Kappa Ltd produces Omega, an animal feed made by mixing and heating three ingredients: Alpha, Beta and Gamma. The company uses a standard costing system to monitor its costs.The standard material cost for $100$ kg of Omega is as follows:Input$($kg$)$Cost per kg$($R$)$Cost per $100$ kg of Omega$($R$)$Alpha BetaGammaTotal$4060201202\mathrm{.}005\mathrm{.}001\mathrm{.}0080\mathrm{.}00300\mathrm{.}0020\mathrm{.}00400\mathrm{.}00$NotesThe mixing and heating process is subject to a standard evaporation loss.Alpha, Beta and Gamma are agricultural products 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.Kappa Ltd has a purchasing manager who is responsible for pricing and supplier contracts.The standard mix is set by the finance i department. The last time this was done was at the product launch, which was five years ago. It has not changed since.Last month $4,600$ kg of Omega were produced, using the following inputs:Input$($kg$)$Alpha BetaGammaTotal$2,2002,500920$Cost per kg$($R$)1\mathrm{.}806\mathrm{.}001\mathrm{.}00$Cost per $100$ kg of Omega $($R$)3,96015,0009205,62019,880$At the end of each month, the production manager receives a standard cost operating statement from Kappa 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 no other feedback on the efficiency of the Omega process.Required:$($a$)$ Calculate the following variances for the last month:$($i$)$the material usage variance for each$($ii$)$ingredient and in total$(4$ marks$)$the total material mix variance$(4$ marks$)($ili$)$ the total material yield variance. $(3$ marks$)($b$)$Discuss the problems with the current system of calculating and reporting variances for assessing the performance of the production manager.