Problem $3(30$ points$)$

Suppose Generic Power Co$.$ manages a repair team to restore power when power lines go down.

There are two men who make up the repair team. This team costs Generic $$125/$hour$.$ But while

power lines are down, it costs Generic Power $$350$ in lost profits.

The two$-$man team can repair a power line in the average time of $40$ minutes. On the average,

there is a new, downed power line once an hour.

Generic is considering two alternatives. One is adding a third man to the repair team. The

hourly cost of the three$-$man team would be $$175.$ This team, however, would be able to repair a

power line in $36$ minutes, on the average.

The other alternative is to hire two additional men who would comprise a second team. Now

each of the two teams can repair a power line in $40$ minutes, and each team costs Generic Power

$$125/$hour$.$

$($a$.)$ For each of the three scenarios, what are the values of $$ and $,$ and how many servers are

there?

$($b$.)$In each of the three scenarios, what is the average number of downed but unrepaired power

lines? $($Also$,$ please note the correct symbol for this.$)$

$($c$.)$ For each of the three scenarios, what are the average total costs that are generated? Which

scenario is the overall least expensive one?