Q 1) The manager of a regional warehouse must decide on the number of loading docks to request
for a new facility in order to minimize the sum of dock costs and driver-truck costs. The manager
has learned that each driver-truck combination represents a cost of $300 per day and that each
dock plus loading crew represents a cost of $1,100 per day.
a) How many docks should be requested if trucks arrive at the rate of four per day, each dock can
handle five trucks per day assuming both rates are Poisson?
b) An employee has proposed adding new equipment that would speed up the loading rate to 6
trucks per day. The equipment would cost $100 per day for each dock. Should the manager invest in the new equipment?
Q 2). The parts department of a large automobile dealership has a counter used exclusively for
mechanics’ requests for parts. The time between requests can be modeled by a negative
exponential distribution that has a mean of five minutes. A clerk can handle requests at a rate of 15
per hour, and this can be modeled by a Poisson distribution that has a mean of 15. Suppose there
are two clerks at the counter.
a.
b.
c.
d.
e. On average, how many mechanics would be at the counter, including those being served?
What is the probability that a mechanic would have to wait for service?
If a mechanic has to wait, how long would the average wait be?
What percentage of time are the clerks idle?
If clerks represent a cost of $20 per hour and mechanics a cost of $30 per hour, what
number of clerks would be optimal in terms of minimizing total cost?
