Name:Aya kurimoto
copy and paste your Excel work in the space below. Do not submit Excel
file.

Question
1 (30 points)
The U.S. Census Bureau
publishes data on factory orders for all manufacturing, durable goods, and
nondurable goods industries. Shown here are factory orders in the United States
from 1987 through 1999 (\$ billion).
(a) Use
these data to develop forecasts for the years 1992 through 2000 using a 4-year
moving average.
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(b) Use
these data to develop forecasts for the years 1992 through 2000 using a 4-year
weighted moving average. Weight the most recent year by 4, the previous year by
3, the year before that by 2, and the year before that by 1.
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By doing the same way, we can get forecasts that are
shown in below

(c) Which
method is more suitable for forecasting factory orders? Hint: Compare the two
methods based on Mean Absolute Deviation (MAD)?.gif” alt=”http://edugen.wiley.com/edugen/courses/crs1396/art/common/pixel.gif”>

Question
2 (40 points)
The following table lists
the worldwide shipments of personal computers (in thousands) according to
Dataquest.

Year

Shipments
(in thousands)

1990

23,738

1991

26,966

1992

32,411

1993

38,851

1994

47,894

1995

60,171

1996

71,065

1997

82,400

1998

97,321

(a) Use
exponential smoothing to determine the forecast of shipments for the year 1999.
Use the actual shipments for 1990 as the starting forecast for 1991. Use a
smoothing constant of.gif”> 0.4.
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(b) Plot
the data, fit a trend line, display equation and.gif”> on the chart anddiscuss the
strength of prediction of the regression model.(Hint:
Use 1990 = 1, 1991 = 2, and so on to get more accurate equation).

(c) Use
the regression model to predict the shipments for the years 1992 through 1999.

(d) Which
forecasting method would you prefer to use and why (Please see residual plot for hint)?
(Note: Compute
MAPE for the two forecasting methods to compare the accuracy for the period
1992-1998).

Problem
3 (30points)
The revenue and cost functions for producing
and selling quantity.gif”> for a certain production facility are given
below.
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a)
Determine the profit function.gif”>.

b)
Use
Excel to graph the functions.gif”> and.gif”> for the interval.gif”>. Copy and paste the graph below. (Hint: Use Scatter plot with smooth lines and markers.)

c)
Compute the break-even quantities.
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d)
Determine the marginal revenue.gif”>.
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e)
Determine the marginal cost.gif”>
f)
.gif”> quantity is the profit maximized?
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below.

Bonus Problem.
(10 points)
Given,
.gif”>
a)
Use the Leibnizâ€™s way to find derivative of the function.
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b)
Find the value of the derivative at.gif”>.
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