$1.$ There are three $(3)$ machines on a production line. Defective rates of the machines are $6\%,5\%,$ and $4\%$ respectively. The employees are afforded $45$ minutes per shift. The plant efficiency is $90\%.$ The plant needs $30000$ good quality products from an $8$hr shift.

$1\mathrm{.}1$ Determine the takt time.

$1\mathrm{.}2$ Given that the scrap costs for pr $1,2,$ and $3$ are R$50,$ R$40$ and R$80$ respectively, calculate the total scrap costs.