A certain workshop does the maintenance for a production plant. The following parameters are applicable:

the service rate per lathe is $5\mathrm{.}5$ jobs$/$week the mean time between failures is $0\mathrm{.}2333$ days the production loss $($Cd$)$ during maintenance is R$500/$week the cost per lathe is as follows o Fixed cost $($Cl$)$ is R$200/$week o Variable cost is

$1)$ the cost for jobs waiting in the queue causes secondary costs of

$($R$500*$traffic intensity$*$ Wq$/$lathe$/$week$)$

$2)$ machine idle time causes secondary cost of $($R$200*$idle

j$)$ Construct a model to calculate the cost C$($n$)$ of the maintenance per week $($week$=7$ days$)$

Calculate in tabular form the total cost of maintenance per week and show the optimum cost. Round off the intermediate values to $3$ decimals. Also show the subcomponents of the calculations in tabular form.