Requested daily quantity for a product is $315$ units $($defect free$).$ The production times $($given as normal time$)$ of the three operations respectively are as follows: Operation a$=1$min; Operation b$=2$min; and Operation c$=3$min. The defect rates is given as $10\%$;$20\%$;$5\%$ for each station in serial. Workers assigned to these operations will accomplish the conversions. The number of workers in the department is limited to $10.$ There are two scenarios:

Scenario I: With Rework

Although the defect rates are given, no product is permitted to leave the plant with any quality defects. Accordingly, all of the defects must be corrected, and the average time to correct the defect is $150\%$ of the initial conversion time $($Example for a$=1$min repair of a$=1*1,5=1,5$min$).$ The same work teams will accomplish this rework. The plant is run as a one$-$shift $9$ hr$/$day $($meal break of $30$ min $($unpaid$)$; Short Breaks $2*15$min; downtime$=35$min$)$ operation. Don$$t forget: The number of workers in the department is limited to $10.$ The performance of employees $1<=$Performance$<=1,25($because of qualified workforce and motivational effect of wage support$).$ A performance below $100\%$ or above $125\%$ is not desired in determining the required number of workers.

Scenario II:Without Rework

There is no rework. The plant is run as a one$-$shift $9$ hr$/$day $($meal break of $30$ min $($unpaid$)$; Short Breaks $2*15$min; downtime$=35$min$)$ operation. Don$$t forget: The number of workers in the department is limited to $10.$ The performance of employees $1<=$Performance$<=1,25($because of qualified workforce and motivational effect of wage support$).$ A performance below $100\%$ or above $125\%$ is not desired in determining the required number of workers.

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