Phone numbers, Social Security numbers, and zip codes are examples of numerical
variables.
The relative frequency of an event is the number of times the event occurs out of the
total number of times the random experiment is run.
We typically choose between a symmetric and skewed distribution on the basis of
practical modeling issues.
Winter’s method is an exponential smoothing method, which is appropriate for a series
with trend but no seasonality.
The expected value of perfect information (EVPI) is irrelevant concept since perfect
information is almost never available at any price.
NARRBEGIN: SA_117_120
A meat market manager for a large grocery store is preparing a processing plan to stock
the shelves with sausage, ground meat, and jerky, which he can prepare from beef, pork
and venison. Sausage and ground meat can be made of any mix of the beef, pork and
venison, as long at the fat contents are below 15% for sausage and 10% for ground
meat. Sausage sells for $5/pound and ground meat sells for $3/pound. Jerky, which sells
or $10/pound, is made in a drying process from beef or venison. In the drying process,
there is a 50% loss in weight for jerky made from beef (e.g., one pound of beef yields
0.5 pounds of beef jerky) and a 30% loss in weight for jerky made from venison. The
market can sell at most 500 pounds of sausage, 1000 pounds of ground meat, and 100
pounds of jerky before their expiration dates. There are currently 1,000 pounds of beef
(10% fat content), 500 pounds of pork (8% fat content), and 200 pounds of venison (2%
fat content) available for processing.
NARREND
Suppose that later in the year, venison will be out of season, but the market will be able
to obtain an additional 300 pounds of pork for the same costs. Develop a processing
plan in that case. How does the solution change?
In financial simulation models, the value at risk (VAR) is the 5th percentile of an output
distribution, and it indicates nearly the worst possible outcome.
If an LP model does have an unbounded solution, then we must have made a mistake ”
either we made an input error or we omitted one or more constraints.
An equation for the random walk model is given by the equation: , where
is the change in the time series from time t to time t ” 1, is a constant, and is
a random variable (noise) with mean 0 and some standard deviation .
Rational decision makers are never willing to violate the expected monetary value
(EMV) maximization criterion when large amounts of money are at stake.
NARRBEGIN: SA_95_96
ABC sells refrigerators. Any refrigerator that fails before it is 3 years old is replaced for
free. Of all refrigerators, 2% fail during their first year of operation; 4% of all
1-year-old refrigerators fail during their second year of operation; and 8% of all
2-year-old refrigerators fail during their third year of operation. It costs ABC $500 to
replace a refrigerator, and ABC sells 6,000 refrigerators per year.
NARREND
Estimate the fraction of all refrigerators that will have to be replaced.
In determining the sample size n for estimating the population proportion p, a
conservative value of n can be obtained by using 0.50 as an estimate of p.
In a nonlinear transformation of data, the Y variable or the X variables may be
transformed, but not both.
Two events A and B are said to be independent if P(A andB)=P(A) +P(B)
NARRBEGIN: SA_91_102
Western Chassis produces high-quality polished steel and aluminum sheeting and two
lines of industrial chassis for the rack mounting of Internet routers, modems, and other
telecommunications equipment. The contribution margin (contribution toward profit)
for steel sheeting is $0.40 per pound and for aluminum sheeting is $0.60 per pound.
Western earns $12 contribution on the sale of a Standard chassis rack and $15
contribution on a Deluxe chassis rack. During the next production cycle, Western can
buy and use up to 25,800 pounds of raw unfinished steel either in sheeting or in chassis.
Similarly, 20,400 pounds of aluminum are available. One standard chassis rack requires
16 pounds of steel and 8 pounds of aluminum. A Deluxe chassis rack requires 12
pounds of each metal. The output of metal sheeting is restricted only by the capacity of
the polisher. For the next production cycle, the polisher can handle any mix of the two
metals up to 4,000 pounds of metal sheeting. Chassis manufacture can be restricted by
either metal stamping or assembly operations; no polishing is required. During the cycle
no more than 2,500 total chassis can be stamped, and there will be 920 hours of
assembly time available. The assembly time required is 24 minutes for the Standard
chassis rack and 36 minutes for the Deluxe chassis rack. Finally, market conditions
limit the number of Standard chassis racks sold to no more than 1,200 Standard and no
more than 1,000 Deluxe. Any quantities of metal sheeting can be sold.
NARREND
What are the decision variables in this problem?
Suppose that after graduation you will either buy a new car (event A) or take a trip to
Europe (event B). Events A and B are mutually exclusive.
NARRBEGIN: SA_51_53
An economic development researcher wants to understand the relationship between the
average monthly expenditure on utilities for households in a particular middle-class
neighborhood and each of the following household variables: family size, approximate
location of the household within the neighborhood, and indication of whether those
surveyed owned or rented their home, gross annual income of the first household wage
earner, gross annual income of the second household wage earner (if applicable), size of
the monthly home mortgage or rent payment, and the total indebtedness (excluding the
value of a home mortgage) of the household.
The correlation for each pairing of variables are shown in the table below:
Table of correlations
NARREND
Which of the variables have a negative linear relationship with the household’s average
monthly expenditure on utilities?
A company is considering investing a total amount of $2.50 million in four bonds. The
expected annual return, the worst-case annual return on each bond, and the “duration”
of each bond are given in the table below.
The duration of a bond is a measure of the bond’s sensitively to interest rates. The
company wants to maximize the expected return from its bond investments, subject to
the following constraints:
The worst-case return of the bond portfolio must be at least 90%.
The average duration of the portfolio must be at most 7
Because of diversification requirements, at most 35% of the total amount invested in a
single bond.
Determine how the company can maximize the expected return on its investment.
