Customers arrive at a hairdresser's salon according to a Poisson process with rate λ = 8 per hour. There are two chairs, and the two hairdressers' service times are exponential random variables with means equal to 15 minutes. Moreover, currently, there is no room where potential customers could wait for their turn to have their hair cut.
(a) The owner considers the possibility of enlarging the salon, so that she could install an additional chair and hire a third hairdresser. This, would increase her operation costs by $20 per hour. If each customer pays $10, would the enlargement be profitable? Justify.
Indication, Calculate the average rate at which customers enter the salon
(b) Another possibility the owner considered consists of enlarging the salon to install a chair where one potential customer could wait to be served. In this case, the increase in operation costs would be equal to $5 per hour. Would this possibility be profitable? Justify.