Directions: This exam consists of seven problems and is an open-book exam
with no time limit. All work should be done individually.Word-process your solutions within this
template and show all steps used in arriving at the final answers. Incomplete
solutions will receive partial credit. Copy and paste all necessary data from
Excel into this document and create tables as needed.
Problem
1
Suppose
a manufacturing company makes a certain item. The time to produce each item is
normally distributed around a mean of 27 minutes with a standard deviation of 2.5
minutes. Thus, the population of production times is normal in shape. Find the
mean and standard deviation of the sample.
Problem
2
The average prices for a product in 12 stores
in a city are shown below.
$2.99,
$2.85, $3.25, $3.55, $3.00, $2.99, $2.76, $3.50, $3.20, $2.85, $3.75, $3.85
Test the hypothesis that the average price is
higher than $2.87. Use level of significancea
= 0.05.
Problem 3
A store wishes
to predict net profit as a function of sales for the next year. The following
table gives the years 1998 to 2005.
|
Year |
Sales (thousands of |
Net Profit |
|
1998 |
51 |
5 |
|
1999 |
55 |
10.2 |
|
2000 |
65 |
9.6 |
|
2001 |
82 |
-3 |
|
2002 |
75 |
2.8 |
|
2003 |
71 |
3.2 |
|
2004 |
82 |
-2.3 |
|
2005 |
81 |
-2.6 |
(a) Graph
the points from 1998 through 2005 on a scatter diagram using Sales as the
independent variable and Net Profit as the dependent variable.
(b) Draw
the regression line on the graph you constructed in Part (a).
(c) What
is the value of the coefficient of determination for this regression model?
Comment on the strength of the regression line for this model.
(d) What
is the predicted net profit for 2006 if sales are expected to be 125?
Problem
4
Last week’s sales of iMac computers at an
Apple Store in Oklahoma City, OK, are shown in the following table:
|
Day |
Sales |
|
1 |
180 |
|
2 |
150 |
|
3 |
210 |
|
4 |
225 |
|
5 |
195 |
|
6 |
190 |
|
7 |
230 |
(a) Use the 3-day
moving average method for forecasting days 4–7.
(b)
Use the 3-day
weighted moving average method for forecasting days 4–7. Use Weight 1 day ago =
2, Weight 2 days ago = 4, and Weight 3 days ago = 3.
(c)
Compare the
techniques using the mean absolute deviation (MAD).
Problem 5
The following table shows six years of average annual cost-of-living
index data:
|
Year |
Annual Cost of Living Index |
|
2008 |
105.8 |
|
2009 |
111.4 |
|
2010 |
121.9 |
|
2011 |
134.3 |
|
2012 |
128.6 |
|
2013 |
125.2 |
(a)
Forecast
the average annual food price index for all years from 2008 to 2013. Use a 3-year
weighted moving average with weights of 0.5, 0.3, and 0.2. Use the largest
weight with the most recent data.
(b)
Forecast
the average annual food price index using exponential smoothing with ?
= 0.7 for all years from 2008 to 2014. Use the rate for 2008 as the
starting forecast for 2008.
(c)
Which
of the methods in parts (a) and (b) produces better forecasts for the 3 years
from 2011 to 2013? Answer on the basis of mean square error (MAD).
Problem
6
A company manufactures two products, Product A
and Product B. The wholesale price and manufacturing cost of each product are
shown below.
|
Item |
Price |
Cost |
Assembly Times (hr) |
|
A |
$30 |
$10 |
2 |
|
B |
$45 |
$15 |
4 |
The company will produce a minimum of 5,000 of
each item. Given the number of hours, the company can sell no more than 8,000
of Item A and 10,000 of Item B. Suppose the company has 50,000 hours of
assembly time available. How many of each item should it produce in order to
maximize profits while meeting all necessary constraints? Give the LP model and
use the graphical method to find the optimal solution.
Problem
7
A commercial real estate company is evaluating
a proposed warehouse. The proposed site is near a rail terminal, but the state
government may extend the highway to the area. In addition, the federal
government is considering rebuilding the local port facilities. Below is the
payoff table in monthly profit depending upon what government actions are
taken. Based on the following criteria, what are the correct choices for
terminal rental?
(a) Optimistic or maximax
criterion
(b) Pessimistic or maximin
criterion
(c) Equally likely or
principle of insufficient reason criterion
|
Warehouse size (ft2) |
Development projects |
|||
|
Rail terminal only |
Highway expansion |
Port rehabilitation |
All |
|
|
15000 |
10 |
25 |
35 |
40 |
|
30000 |
15 |
25 |
40 |
50 |
|
60000 |
20 |
30 |
45 |
75 |
|
100000 |
15 |
20 |
40 |
90 |
