A$).$ Taylor$$s Woodworks plant produces wooden packing boxes to be used in the local seafood industry. Current operations allow the company to make $500$ boxes per day, in two $8-$hour shifts $(250$ boxes per shift$).$ The company has introduced some small changes in equipment, and conducted appropriate job training, so that production levels have risen to $400$ boxes per shift. These changes did not require any change in the amount of capital spending or energy use. What is the firm's new labor productivity? $(4$ marks$)$

B$)$ Parkinson Products produces cast bronze valves for use in offshore oil platforms. Currently, Parkinson produces $1600$ valves per day. The $20$ workers at Parkinson work from $7$ a$.$m$.$ until $4$ p$.$m$.,$ with $30$ minutes off for lunch and a $15-$minute break during the morning work session and another at the afternoon work session. Parkinson is in a competitive industry and needs to increase productivity to stay competitive. They feel that a $20$ percent increase is needed.

Parkinson'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. $(4$ marks$)$

$($b$)$ Calculate labor productivity for the hypothetical $20$ percent increase. $(4$ marks$)$

$($c$)$ What is the productivity after the change in work rules? $(4$ marks$)$

$($d$)$ Write a short paragraph analyzing these results. $(2$ marks$)$

C$).$ Compute the multifactor productivity measure for an eight$-$hour day in which the usable

output was $500$ units, produced by three workers who used $600$ pounds of materials.

Workers have an hourly wage of $$20,$ and material cost is $$1$ per pound.

Overhead is $1\mathrm{.}5$ times labour cost.