The Cool$-$Tech Company produces various types of fans. In May, the company produced $1,728$ window fans at a standard price of $$40\mathrm{.}00.$ The company has $12$ direct labor employees. During May, window fans were produced on $9$ working days $($of $8$ hours each$),$ and other products were produced on other days. Determine the labor productivity of the window fans. $(1$ point$)$

The Cool$-$Tech Company $($see $1$ above$)$ also produces desk fans at a standard price of $$25\mathrm{.}00.$ During May, $1,872$ desk fans were produced on $11$ working days $($of $8$ hours each$).$ On one day, two employees called in sick. $(2$ points$)$

a$.$ Determine the labor productivity of the desk fans.

b$.$ Was productivity higher for the window fans or for the desk fans in May?

Here is additional information about the Cool$-$Tech Company $($see $1$ & $2).$ There were $20$ working days in May, during which the compensation for a Cool$-$Tech direct labor employee $($including wages and fringe benefits$)$ amounted to $$21\mathrm{.}00$ per hour. The direct material cost of window fans is $$7\mathrm{.}00$; the direct material cost of desk fans is $$5\mathrm{.}00.$ The annual overhead expense incurred in operating the factory is $$600$ per working day, $(2$ points$)$

a$.$ Determine the multi$-$factor productivity of the Cool$-$Tech Company in May.

b$.$ What is the interpretation of the multi$-$factor productivity?

In June, the Cool$-$Tech Company produced $1,730$ window fans $($see $1)$ in $10$ working days. No employees were absent during that time period. What was the percentage change in labor productivity of window fans from May? $(1$ point$)$

A process currently produces $85\%$ good units with a successful rework rate of $40\%.$ Daily input to the process is $500$ units. If the process improves its percentage of good units produced to $95\%,$ while leaving its rework percentage unchanged, what is the increase in the daily yield of the process? $(4$ points$)$