comparisons and operations
Comparing costs: internet providers
Over the last years more and more people are connecting to the
Internet using a personal computer and a modem.
Some people connect for only a few minutes
a day, to send and receive e-mail. Others connect for
several hours a day to surf the net.
Businesses and institutions need to be connected to the
Internet all the time.
To connect to the Internet one must sign-up with an
Internet Service Provider (ISP). ISPs use
different ways to charge their fees. In the following task
examine two such fee structures, proposed by two
competing ISPs. Investigate the consequences
of changing the fees to help a company
plan a fee reduction that will attract new customers.
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Compare the fees charged by two ISPs.
Each one charges a daily fee based on
the amount of time the user is connected to the Internet.
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| daily fee (dollars) |
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daily hours of usage |
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The InterLine company charges a fixed daily fee of
30 cents. On days on which the user does not connect to the
Internet, no fee is charged. In addition, the company charges
14 cents per hour of connection.
The Parabolic company does not charge a fixed
daily fee. Payment for the first
hour of usage is 24 cents,
for the second hour 23 cents, for the
third hour 22 cents, and so on. The following correspondence rule describes the
dependence of Parabolic's daily charges (in dollars), on the number of hours
of usage:
f(x)=x(49-x)/200.
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The two companies are competing for customers,
and one of them wants to reduce its fee
to draw customers away from its competitor.
Here are some proposed methods of cost reduction:
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Reducing daily charges by a fixed amount (for example:
"80 cents off each day").
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Offering some free time every day (for example:
if the free time is 30 minutes, users connecting
for 2 hours will as if they had been connected for 1.5 hours).
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Reducing the clock rate (for example:
if the clock rate is reduced by a factor of 2, users
connecting for one hour will pay as if they had been
connected for 30 minutes).
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Offering a discount of a certain percentage (for example:
reducing the fee by 20%).
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Offering a reduction of the daily fee depending
on how long users are connected (for example:
5 cents off the first hour, 10 cents off the second hour, etc.).
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One of the ISPs is soliciting your advice
Advise the ISP how to reduce
fees in order to draw away customers from its
competitor. Prepare a report and
present several proposals for changing the fees.
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Describe the current situation, before the fee reduction: which customers will prefer each of the ISPs?
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Present several examples for changing the
fees of the company you are advising. Explain your
proposal in words as well as in the mathematical terms of
"changing a function."
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Explain why your proposals will attract
customers away from the competing company.
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Discuss the advantages and disadvantages of
your proposal. Is there one
proposal that you prefer over the others?
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Consider the possibility that
the competing ISP
will imitate your method and offer a reduction of the same
type as the one you proposed for your client. What will
the situation be in this case?
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