Question: A fast-food chain is opening a new restaurant in a shopping mall. The restaurant needs to hire a cashier and has two prime candidates. Candidate 1 is experienced and fast but demands a higher salary. Candidate 2 is inexperienced and slower but also has more modest salary claims. The question is which one the restaurant manager should choose. Both candidates can be considered to have exponentially distributed service times, candidate 1 with a mean of 1 min and candidate 2 with a mean of 1.5 min. The customers arrive according to a Poisson process with a mean of 30 customers/h.
The waiting cost has been estimated to $6 per minute for each customer until they have been fully served and have paid for their meal. Determine the maximum difference in monthly salary that would justify hiring candidate 1 instead of candidate 2 when the objective for the restaurant manager is to minimize the expected total cost. Assume that there are 30 workdays in a month and each workday is 8 h long.