Using time$-$study techniques, an observer studies the placement of a $2-$foot by$8-$foot wall forms for a straight wall. Three carpenters are employed, and the observer breaks down the overall work process into the following operations:

$$ Operation $1$: Carpenters walk to get form. Operation $2$: Carpenters pick up form. Operation $3$: Carpenters take form to placement location. Operation $4$: Carpenters position and put form in place. The following times in seconds are collected for each of $8$ cycles.

Assuming a rating factor of $1\mathrm{.}1$ and an allowance factor of $\mathrm{.}15,$ solve each of the following problems:

$($a$)$ Calculate a standard time in seconds per cycle.

$($b$)$ Calculate the standard time productivity in terms of carpenter$-$hour per square foot of contact area.

$($c$)$ Assume that the estimator thinks that Operation $3$ can be reduced by one$-$half the allotted time, and recalculate the standard time for the process.