Customers Arrive at a Fast Food Restaurant with One Server

question 3

Essay

Customers arrive at a fast food restaurant with one server according to a Poisson process at a mean rate of 30 per hour.The server has just resigned,and the two candidates for the replacement are X (fast but expensive)and Y (slow but inexpensive).Both candidates would have an exponential distribution for service times with X having a mean of 1.2 minutes and Y having a mean of 1.5 minutes.Restaurant revenue per month is given by $6,000/W where W is the expected waiting time (in minutes)of a customer in the system.Determine the upper bound on the difference in their monthly compensations that would justify hiring X rather than Y.

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Definitions:

Straight Line

The shortest distance between any two points, or a line with a constant slope, in geometric terms.

Opportunity Costs

Opportunity costs represent the benefits an individual, investor, or business misses out on when choosing one alternative over another.

Natural Disaster

A sudden and extreme event caused by natural processes of the Earth that can result in significant damage and loss.

Inward Shift

A decrease in the potential output of a good or service, often represented by a shift to the left of its supply or demand curve.