$2$ A work group of $10$ workers in a certain month produced $7200$ units of output working $8h\frac{r}{?}$ day for $22$ days in the month. Determine the labor productivity ratio using $($a$)$ units of output per worker$-$hour and $($b$)$ units of output per worker$-$month. $($c$)$ Suppose that in the next month, the same work group produced $6800$ units but there were only $20$ workdays in the month. For each productivity measure as in $($a$)$ and $($b$),$ determine the productivity index for the next month using the prior month as a base.