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A construction company is preparing for a nine-month project, and will need to develop
a staffing plan. The company can assign up to 30 of its own full-time employees to the
project, and will hire short-term contract employees to make up any shortage in meeting
the personnel requirements. Company employees earn $6,000 per month, while
short-term contract employees make $8,600/month. Contract employees can be
assigned to the project beginning in any month, and their contract period is two months.
The number of workers required for the project by month is shown below:
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Suppose the bonus for completing the project three months early is $250,000. What
would be the net bonus to the company, after adjusting for any difference in personnel
costs under the accelerated schedule?
A 0-1 variable, also called a binary variable, is a variable that must equal 0 or 1.
The p-value of a test is the smallest level of significance at which the null hypothesis
can be rejected.
In a single-stage decision problem, a single decision is made first, and then all
uncertainty is resolved.
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A company is about to develop and then market a new product. It wants to build a
simulation model for the entire process, and one key uncertain input is the development
time, which is measured in an integer number of months. For each of the scenarios in
the questions below, choose an “appropriate” distribution, together with its parameters,
and explain your choice.
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Company experts believe the development time will be from 5 to 9 months, but they
have absolutely no idea which of these will result.
A fairly recent alternative to algebraic modeling is spreadsheet modeling. Instead of
relating various quantities with algebraic equations and inequalities, we relate them in a
spreadsheet with cell formulas.
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An automobile manufacturer needs to buy aluminum sheets with an average thickness
of 0.05 inch. The manufacturer collects a random sample of 40 sheets from a potential
supplier. The thickness of each sheet in this sample is measured (in inches) and
recorded. The information below are pertaining to the Chi-square goodness-of-fit test.
Test of normal fit
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(A) Are these measurements normally distributed? Summarize your results.
(B) Are there any weaknesses or concerns about your conclusions in (A)? Explain
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The height of a typical American male adult is normally distributed with a mean of 68
inches and a standard deviation of 5 inches. We observe the heights of 12 American
male adults.
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Let Y be the number of the 12 male adults who are less than 62 inches tall. Determine
the mean and standard deviation of Y.
Tyson Manufacturing (a maker of industrial products) is interested in marketing a new
product. The company must decide whether to manufacture this product essentially on
its own or employ a subcontractor to manufacture it. Below are two tables that represent
the information related to the estimated probability distribution of the cost of one unit
of this product under each alternative.
Cost under “Make” alternative. Cost under “Buy” alternative.
Cost per unit Probability Cost per unit Probability
$40 0.20 $40 0.15
$45 0.25 $45 0.30
$50 0.35 $50 0.40
$55 0.20 $55 0.15
Assuming that Tyson seeks to minimize the expected unit cost of manufacturing of
buying the new product, should the company make the new product or buy it from a
subcontractor? Show your work.
An outlier is an observation that falls outside of the general pattern of the rest of the
observations on a scatterplot.
When formulating a linear programming spreadsheet model, there is a set of designated
cells that play the role of the decision variables. These are called the objective cells.
In the multiple regression model we interpret X1 as follows:
holdingX2 constant, if X1 increases by 1 unit, then the expected value of Y will increase
by 9 units.
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Below you will find summary measures on salaries for classroom teachers across the
United States. You will also find a list of selected states and their average teacher salary.
All values are in thousands of dollars.
Salaries for classroom teachers across the United States
Selected states and their average teacher salary
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Which of the states listed paid their teachers average salaries that are below 75% of all
average salaries?
A histogram is said to be symmetric if it has a single peak and looks approximately the
same to the left and right of the peak.
The mean is a measure of central location.
The partial F test is a procedure to determine whether extra variables in a group provide
any extra explanatory power in the regression equation