Problem Set
8
B.7 The Attaran Corporation manufactures two electrical
products: portable air conditioners and portable heaters. The
assembly process for each is similar in that both require a certain
amount of wiring and drilling. Each air conditioner takes 3 hours
of wiring and 2 hours of drilling. Each heater must go through 2
hours of wiring and 1 hour of drilling. During the next production
period, 240 hours of wiring time are available and up to 140 hours
of drilling time may be used. Each air conditioner sold yields
a profit of $25. Each heater assembled may be sold for a $15
profit. Formulate and solve this LP production-mix situation, and
find the best combination of air conditioners and heaters that
yields the highest profit. D.1 Customers arrive at Rich Dunns Styling Shop at a rate
of 3 per hour, distributed in a Poisson fashion. Rich can perform
haircuts at a rate of 5 per hour, distributed
exponentially.
D.9 Neve Commercial Bank is the only bank in the town of
York, Pennsylvania. On a typical Friday, an average of 10 customers
per hour arrive at the bank to transact business. There is
currently one teller at the bank, and the average time required to
transact business is 4 minutes. It is assumed that service times
may be described by the exponential distribution. If a single
teller is used, find:
CEO Benjamin Neve is considering adding a second teller (who
would work at the same rate as the first) to reduce the waiting
time for customers. A single line would be used, and the customer
at the front of the line would go to the first available bank
teller. He assumes that this will cut the waiting time in half. If
a second teller is added, find the new answers to parts (a) to (e).
Purchase the answer to view it
B.1, B.5, B.7, D.1, and D.9 (parts a through e; assume µ
=
15)
B.1 Solve the following linear programming problem
graphically:
B.5 Solve the following LP problem
graphically:
a) Find the average number of
customers waiting for
haircuts.
b) Find the average number of
customers in the
shop.
c) Find the average time a
customer waits until it is his or her turn.
d) Find the average time a
customer spends in the shop.
e) Find the percentage of time
that Rich is
busy.
arrival
time 6
processing
time 4
exponential
distribution 1
CV
factor 1
Utilization 0.67
Utlization
factor 2
a) The average time in the
line.
b) The average number in the line.
c) The average time in the system.
d) The average number in the system.
e) The probability that the bank is empty
With one more teller added
utilzation
utilzation factor
a) The average time in the line.
b) The average number in the line.
c) The average time in the system.
d) The average number in the system.
e) The probability that the bank is empty
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