A New Shopping Mall Is Considering Setting Up an Information

question 59

Essay

A new shopping mall is considering setting up an information desk operated by two employees.Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 20 per hour.It takes an average of 4 minutes to answer a question.It is assumed that arrivals are Poisson and answer times are exponentially distributed.
(a)Find the proportion of the time that the employees are busy.
(b)Find the average number of people waiting in line to get some information.
(c)Find the expected time a person spends just waiting in line to have his question answered.

---

Definitions:

Unbounded Problem

A scenario in optimization where the solution can infinitely improve, meaning there are no constraints limiting the value of the objective function.

Objective

A goal or target that is aimed to be achieved, usually specific, measurable, and time-bound.

Without Bound

An expression indicating that there is no limit or boundary to a certain condition or value.

Time Constraint

A specific limit or period within which a task or project must be completed.