The document discusses several forces that are transforming manufacturing, including smart products/connectivity, servitization, digitization, personalization, and globalization. It notes that 68% of manufacturers expect major business transformations in the next 3 years due to these factors. Manufacturers must rethink how products are conceived, designed, produced, sold and serviced. The goal is to not only make better products but also make manufacturing processes better through continual improvement and feedback. While traditional large-scale manufacturing may not return to Detroit, the auto industry still has opportunities to take advantage of these transforming forces.

1. The Forces That Are Transforming How Products Are Made
Beth Ambruch , PTC
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Things are looking up for the Big Three auto makers. Ford,
General MotorsGM +0.45%, and Chrysler all posted a
significant uptick in July sales. But the old-style factories of the
Detroit golden era have long since gone, and they’re not coming
back, at least according to a recent article in TheWashington
Times.
Whether we like it or not, globalization has been a major factor
in the staying power of the auto industry and other major
manufactures. The practice of scattering production, jobs and
plants across the globe has delivered great benefits to the
consumer and the manufacturer. Companies have been able to
squeeze as much efficiency as possible from the products they
make so that what we desire is affordable and readily available.
This has been the definition of success for many decades.
Yet with the growing costs and challenges associated with the
global market, many manufacturers are looking for new sources
of competitive advantage.
Global industry is in the midst of a fundamental transformation
– having to rethink everything from how products are
conceived, designed and sourced to how they are produced, sold
and serviced. In fact, according to a recent study done by
Oxford Economics, a global forecasting and quantitative
analysis firm, 68 percent of 300 manufacturers surveyed expect
to undergo major business transformation in the next three
years.
What is this force driving change? To be certain, it’s not just
one, but a confluence of factors changing the manufacturing
landscape. Digitization, personalization, “smart” products,
connectivity, and servitization are some key drivers, and

2. globalization and regulation continue to drive manufacturing
businesses, but in new ways.
· Smart Products & Connectivity. By 2020 more than 50 billion
devices are expected to be connected to a global network. In
this new era of connectivity, every day physical objects will be
able to identify themselves and communicate directly with other
devices. This one single ability leads directly to a new level of
customer service, termed “servitization”.
· Servitization. Again from Oxford Economics, more than two-
thirds of manufacturers expect to use service as a differentiator
by 2015, with more than half of them planning to establish a
service profit center, and 77 percent indicating that improving
services is a key factor for competitiveness. In this new era,
manufacturers need to look beyond the single product sale
transaction into a new relationship between themselves and the
consumer—characterized by an ongoing delivery of value—
exchanged over a platform in the form of a smart, connected
product.
· Digitization. To better meet fragmenting customer demand,
manufacturers are harnessing digital technologies that help them
improve global collaboration and expand regional
manufacturing processes into globalized design-build-service
anywhere strategies. Digital technologies also enable
manufacturers to simulate and validate many product
configurations before they are built.
· Personalization. As consumer demand continues to evolve,
manufacturers are being pressured to respond with increasing
customer choice. But product diversity can increase cost, and
potential decrease quality. According to the Oxford Economics
report, over two-thirds of manufacturing executives will apply
Voice of Customer to better understand their customers, and to
make certain quality does not suffer.
· Globalization. The global market continues to expand, and it’s
not just about where we manufacture and source materials
anymore. Manufactures must be able to design, build, service,
and sell to and from anywhere.

3. · Regulation. With globalization comes responsibility.
Manufacturers must stay ahead of the always changing
regulatory requirements and of local customs related to health,
safety, trade and the environment. Sixty-three percent of C-
level executives say global product compliance will be the most
developed to coordinate strategy and planning.
The goal for every manufacturer should not only be to “make
better things”—creating products and services that meet
customer needs, but also to “make things better,” facilitating the
engineering, service planning and execution, management and
production processes through which innovation can evolve from
conception to retirement, and creating a closed feedback loop to
ensure continual improvement and alignment across the
business.
For many manufacturers this is a succeed or fail moment, they
can choose to get ahead of the change by seizing the
opportunities presented by tomorrow’s world or get run over by
newcomers trying to disrupt the market by adapting their
strategies accordingly.
While TheWashington Times article was right in the sense that
traditional large-scale manufacturing is unlikely to return to
Detroit. The Big Three have numerous opportunities to take
advantage of these forces to create a stronger, more interesting
opportunity. And perhaps, with this manufacturing
transformation, will come a new era powerful enough to bring
fresh jobs and opportunities back to the United States.
Name __________________________ Differential Equations
Problem Set Score ______
Show all work neatly done in pencil, or typed, if possible.

4. 1. Solve the initial value problem.
a) kP
dt
dP
= 100
0
=P
b)
3
4
1
ydx
dy
= ( ) 10 =y

5. c) 32 −= y
dx
dy
( ) 20 =y
d) ( )xx
dt
dx
−= 53 ( ) 80 =x
2. In a certain culture of bacteria, the number of bacteria
increased tenfold in 10 hours. Assuming natural

6. growth, how long did it take for their number to double?
3. The half-life of radioactive cobalt is 5.27 years. Suppose
that a nuclear accident has left the level of cobalt
radiation in a certain region at 100 times the level acceptable
for human habitation. How long will it be
before the region is again habitable?
4. In 1998 there were 40 million Internet users in the world and
this number was then doubling every 100 days.
Assuming that this rate of growth continued, how long would it
be until all the world’s 6 billion human
beings were using the Internet?

7. 5. The population of a certain prolific breed of rabbits
satisfies the initial value problem
2
kP
dt
dP
= .
Initially there are only 2 rabbits (a male and a
female) and after 3 months there are 4 rabbits. How
many rabbits will there be after 6 months?
6. Consider a rabbit population ( )tP satisfying the logistic
equation 2bPaP
dt
dP
−= , where aPB = is the time
rate at which births occur and

8. 2
bPD = is the rate at which deaths occur. If the initial
population is 240
rabbits and there are 8 births per month and 6 deaths per month
occurring at time 0=t , how many months
does it take for ( )tP to reach 95% of the limiting population
M?
7. If a Modern pizza is cooling in a medium with a constant
temperature A, then according to Newton’s Law of
Cooling the rate of change of temperature T of the pizza is
proportional to T – A. We plan to cool the pizza

9. initially at C
o
80 by setting it on the front porch, where the temperature is .0
C
o
If the temperature of the
pizza drops to C
o
50 after 10 minutes, when will it be C
o
40 ( )Fo104 and ready to eat?
8. Just before midday the body of an apparent homicide victim
is found in a room that is kept at a constant
temperature of .70 F
o
At 12 noon the temperature of the body is F
o
80 , and at 1pm it is .75 F

10. o
Assume
that the temperature of the body at time of death was F
o
6.98 and that it has cooled in accordance with
Newton’s law of cooling. What was the time of death?
Whodunnit???
9. Orange, CT. has a fixed population of 10,000 people. On
January 1, 1000 people have the flu. On April 1,
2000 people have the flu. Assume that the rate of increase of the
number ( )tN who have the flu is
proportional I the number who don’t have it. How many will
have the disease on October 1?

11. 10. Suppose that the population ( )tP (in millions) in
Mauritania satisfies the differential equation
( )PkP
dt
dP
−= 200 . Its population in 1960 was 100 million and was
growing at a rate of 1 million per year.
Predict the country’s population in 2010.

12. Extra Credit
1. Suppose that a community contains 15,000 people who are
susceptible to Michaud’s syndrome, a contagious
disease. At time 0=t the number ( )tN of people who have
developed Michaud’s syndrome is 5000 and is
increasing at the rate of 500 per day. Assume that ( )tN ′ is
proportional to the product of the numbers of
those who have caught the disease and of those who have not.
How long will it take for another 5000 people
to develop Michaud’s syndrome?