Workers in a certain industry produce $$120$ of value in an eight$-$hour da$,$ workers' daily wages $($regardless of number of hours worked in a day$)$ are $$50$ and the costs of materials plus the daily wear and tear on machines each worker uses is $$20.$

a$.$ If the working day increases from $8$ to $12$ hours, the daily value each worker produces becomes $ $,$ the daily wear and tear on machines is $ per worker and the surplus value per worker is $

b$.$ The lengthening of the workday means that the rate of exploitation from