The first alternative is to add side boards to the trucks$($so that more material could be$$ loaded$)$ and to add a helper at the loading station$($so that filling time could be$$ reduced$)$ at a total cost of$$ $$50,000.$ The arrival rate of trucks would change to five per$$ hour, and the filling time would be reduced to $4$ minutes. The second alternative is to add another loading station at a cost of$$ $$80,000.$ The trucks would wait in a common line and the truck at the front of the line would move to the next available station.

Part $2$

The average waiting time in the system under the current system is

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$12\mathrm{.}00$ minutes. $($Enter your response rounded to two decimal$$ places.$)$

Part $3$

The average waiting time in the system for the first alternative is

$$