C ASE PRO B L E M 2: M c NEIL’S A UTO M ALL
Harriet McNeil, proprietor of McNeil’s Auto Mall, believes that it
is good business for her atuomobile dealership to have more
customers on the lot than can be served, as she believes this
creates an impression that demand for the automobiles on her lot is
high.
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Case Problem 3: Grievance Committee at Tuglar Corporation 273
However, she also understands that if there are far more customers
on the lot than can be served by her salespeople, her dealership
may lose sales to customers who become frustrated and leave without
making a purchase. Ms. McNeil is primarily concerned about the
staffing of salespeople on her lot on Saturday mornings (8:00 a.m.
to noon), which are the busiest time of the week for McNeil’s Auto
Mall. On Saturday mornings, an average of 6.8 customers arrive per
hour. The customers arrive randomly at a constant rate throughout
the morning, and a salesperson spends an average of one hour with a
customer. Ms. McNeil’s experience has led her to conclude that if
there are two more customers on her lot than can be served at any
time on a Saturday morning, her automobile dealership achieves the
optimal balance of creating an impression of high demand without
losing too many customers who become frustrated and leave without
making a purchase. Ms. McNeil now wants to determine how many
salespeople she should have on her lot on Saturday mornings in
order to achieve her goal of having two more customers on her lot
than can be served at any time. She understands that occasionally
the number of customers on her lot will exceed the number of
salespersons by more than two, and she is willing to accept such an
occurrence no more than 10% of the time.
Suppose Ms. McNeil currently uses five salespeople on her lot on Saturday morning. Using the probability distribution you identified in (1), what is the probability that the number of customers who arrive on her lot will exceed the number of salespersons by more than two? Does her current Saturday morning employment strategy satisfy her stated objective? Why or why not? and What is the minimum number of salespeople Ms. McNeil should have on her lot on Saturday mornings to achieve her objective?
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