You are evaluating a potential work cell setup. It is a mill operation that runs for $15$ minutes. The operator spends $\frac{21}{2}$ minutes removing the finished part and putting a new piece in the fixture. The worker is paid $$\frac{15}{h}r.$ You have estimated that the worker would spend $45$ seconds traveling from one machine to another. The accountants predict that each mill will cost $$\frac{25}{h}r$ to run. Based on lowest cost, how many machines should you use in your cell if you only use the one worker? What would happen to the cost if you reduced setup time by $30$ seconds?

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A $5$ person production line has the following characteristics per station:

$\backslash$table$[[$OPERATOR$,$Standard Minutes$],[1,1\mathrm{.}90],[2,1\mathrm{.}65],[3,1\mathrm{.}50],[4,1\mathrm{.}80],[5,2\mathrm{.}00]]$

What is the efficiency of this line? How many operators do we need if we want the output from the line to be $550$ units$/$day$?$ How many will we need for the same rate of production if our improvements eliminate six seconds from operation #$1$ along with $12$ seconds from operation #$5?[$Show all of your work$]$