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2009年美国大学生数学建模竞赛原题以及翻译,重点突出。
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2009 B:Energy and the Cell Phone
This question involves the “energy” consequences of the cell phone revolution. Cell
phone usage is mushrooming, and many people are using cell phones and giving up
their landline telephones. What is the consequence of this in terms of electricity use?
Every cell phone comes with a battery and a recharger.!
Requirement 1
Consider the current US, a country of about 300 million people. Estimate from
available data the number!H!of households, with!m!members each, that in the past
were serviced by landlines. Now, suppose that all the landlines are replaced by cell
phones; that is, each of the!m!members of the household has a cell phone. Model the
consequences of this change for electricity utilization in the current US, both during
the transition and during the steady state. The analysis should take into account the
need for charging the batteries of the cell phones, as well as the fact that cell phones
do not last as long as landline phones (for example, the cell phones get lost and
break).!
Requirement 2
Consider a second “Pseudo US”—a country of about 300 million people with about
the same economic status as the current US. However, this emerging country has
neither landlines nor cell phones. What is the optimal way of providing phone service
to this country from an energy perspective? Of course, cell phones have many social
consequences and uses that landline phones do not allow. A discussion of the broad
and hidden consequences of having only landlines, only cell phones, or a mixture of
the two is welcomed.!
Requirement 3
Cell phones periodically need to be recharged. However, many people always keep
their recharger plugged in. Additionally, many people charge their phones every
night, whether they need to be recharged or not. Model the energy costs of this
wasteful practice for a Pseudo US based upon your answer to Requirement 2. Assume
that the Pseudo US supplies electricity from oil. Interpret your results in terms of
barrels of oil.!
Requirement 4
Estimates vary on the amount of energy that is used by various recharger types (TV,
DVR, computer peripherals, and so forth) when left plugged in but not charging the
device. Use accurate data to model the energy wasted by the current US in terms of
barrels of oil per day.!
Requirement 5
Now consider population and economic growth over the next 50 years. How might a
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