Gibson's management believes that the $20$ percent increase will not be possible without a change in working

conditions, so they change work hours. The new schedule calls on workers to work from $7$:$30$ a$.$m$.$ until $4$:$30$

p$.$m$.,$ during which workers can take one hour off at any time of their choosing. Obviously, the number of paid

hours is the same as before, but production increases, perhaps because workers are given a bit more control over

their workday. After this change, valve production increased to $1800$ units per day.

$($a$)$ Calculate labor productivity for the initial situation.

$($b$)$ Calculate labor productivity for the hypothetical $20$ percent increase.

$($c$)$ What is the productivity after the change in work rules?

$($d$)$ Analyze the results from OM$$s perspective.