The Registration Area Has Just Opened at a Large Convention

question 120

Essay

The registration area has just opened at a large convention of building contractors in Banff. There are 300 people arriving per hour (Poisson distributed), and the cost of their waiting time in the queue is valued at $120 per person per hour. The local convention bureau provides servers to register guests at a fee of $20 per person per hour. It takes about 1.5 minutes to register an attendee (exponentially distributed). A single waiting line, with multiple servers, is set up.
a) What is the minimum number of servers for this system?
b) What is the optimal number of servers for this system?
c) What is the cost for the system, per hour, at the optimum number
of servers?
d) What is the server utilization rate with the minimum number of
servers?

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Definitions:

Fast-Food Industry

The fast-food industry comprises businesses that serve quick service food items over the counter or via drive-thrus, often emphasizing speed, convenience, and affordability.

Marginal Revenue

The additional income generated from selling one more unit of a good or service.

Total Revenue

Total Revenue is the full amount of income generated by the sale of goods or services before any costs are deducted.

Perfectly Elastic Demand

Demand in which quantity drops to zero at the slightest increase in price.