MG 787 Quiz 1 | Course Paper

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A correlation of 0 indicates that the two variables have no linear relationship with each

other.

For any sample of fixed size n, the true standard deviation of the sampling distribution

of the mean is the standard deviation of the population.

A constraint function is a function of the decision variables in the problem.

Nonnegativity of the decision variables is an example of an explicit constraint.

When interpreting sensitivity analysis information for changes in model parameters, all

other model parameters are held constant.

Below is the spreadsheet for an economic order quantity model.

Assume that the distribution of demand is normal with a mean of 20,000 and standard

deviation of 2,000.The increase in total cost is calculated by adding the holding cost

and the ordering cost.

In stock trading, the higher the coefficient of variation for the stock, the smaller the

relative risk is for the return provided.

In association analysis, the antecedent and consequent are sets of items that do not have

any items in common.

The value of a coefficient of skewness falling between 0.5 and -0.5 indicates relative

symmetry.

Any solution that satisfies all constraints of a problem is called a feasible solution.

In a MATCH function, the default value for match_type = 0.

Stone Age Surfboards is a small manufacturer of two types of popular low-tide

surfboards, the Graystone and the Lava models. The manufacturing process consists of

two departments: fabrication and finishing. The fabrication department has 8 skilled

workers, each of whom works 9.25 hours per day. The finishing department has 5

workers, each of whom works a 6 -hour shift per day. Each pair of Graystone

surfboards requires 2.5 labor hours in the fabrication department and 2 labor hours in

finishing. The Lava model requires 4.2 labor-hours in fabrication and 3.6 labor-hours in

finishing. The company operates 6 days a week. It makes a per unit profit of $40 on the

Graystone model and $60 on the Lava model. The company anticipates selling at least

twice as many Lava models as Graystone models.

Use the spreadsheet below for Stone Age Surfboards to answer the following

question(s) using integer constraints on variables in the optimization models using the

standard Solver.

What is the total number of hours used for fabrication?

A) 39.6

B) 34.4

C) 29.2

D) 24.8

Pickson Luthiers Corporation is studying where to locate a phone charging point on the

factory floor. The locations of five production cells are expressed as X– and

Y-coordinates on a rectangular grid of the factory layout. The daily demand for the

charging point (measured as the number of trips to the charging point) at each

production cell is also known. Because of the nature of the equipment layout in the

factory and for safety reasons, workers must travel along marked horizontal and vertical

aisles to access the charger. Thus, the distance from a cell to the charger is measured as

rectilinear distance.

The table below provides the relevant information.

The optimal location should minimize the total weighted distance between the charging

point and all production cells, where the weights are the daily number of trips to the

phone charging point.

According to the model, which of the following is the weighted distance between the

phone charger and Measurements cell?

A) 12.00

B) 75.00

C) 7.00

D) 54.00

Which of the following is true about using sample data?

A) All samples have the same characteristics and hence always adequately represent the

underlying population.

B) It can limit the ability to predict uncertain events that may occur because potential

values outside the range of the sample data are not included.

C) It is better to use sample data than trying to identify the underlying probability

distribution and fitting a theoretical distribution to it.

D) Using sample data in a decision model increases the ability to predict uncertain

events.

Jonathan Reese is considering three stocks in which to invest with a fixed budget. The

table below provides information on Jonathan’s expected returns for each stock. The

table also provides information, collected from market researchers, on the

variance-covariance matrix of the individual stocks. He expects a total return of at least

10%.

Develop a quadratic optimization model to find the optimal allocation of the budget to

each stock, and variance calculations for squared terms and cross-products based on the

variance-covariance matrix.

According to the model, what percentage of the budget should be allocated to Stock 1?

A) 10%

B) 25%

C) 50%

D) 40%

One of the measures of location is calculated as 88. Which of the following measures of

location corresponds to this value?

A) mean

B) mode

C) median

D) midrange

Which of the following is true of covariance, between two variables, when one of the

deviations from the mean is positive and the other is negative?

A) the degree of linear association is high between the two variables

B) there is no covariance between the two variables

C) the covariance will be negative

D) the covariance will be positive

Which of the following accurately describes a sampling distribution of the mean?

A) It is the mean of any one sample from a group of related populations of different

sizes.

B) It is the mean distribution of any one sample from a group of samples of varying

sizes from a population.

C) It is the mean of half the samples from a related group of populations.

D) It is the distribution of the means of all possible samples of fixed size n from a

population.

Which of the following is true of normal distributions?

A) The mean, median, and mode are all equal.

B) Its measure of skewness is always greater than 1.

C) The range of the random variable X is bounded.

D) Mathematical formulas make it easier to compute normal distributions.

Below is the spreadsheet for an economic order quantity model.

Assume that the distribution of demand is normal with a mean of 20,000 and standard

deviation of 2,000.

What is the coefficient of variation obtained from the simulation results?

A) 0.28

B) 0.10

C) 0.45

D) 0.60

The table provided below gives the sales details of the number of android smart phones

at an electronic retail store for the past 6 weeks. The time series appears to be relatively

stable, without trend, seasonal, or cyclical effects. (Hint: Optimize Î± value in 0.1

increments)

Calculate the value of the mean absolute percentage error for the given data.

A) 20.90

B) 16.60

C) 21.72

D) 29.97

In the spreadsheet below, there is data on the price, cost, demand, and quantity

produced for an item. There are also different “what if” values that can help a manager

to calculate costs and revenue with variability in demand.

Calculate the total revenue when the quantity produced is 55,000 and demand is 60,000.

A) $1,375,000

B) ($1,320,000)

C) $1,430,000

D) $2,750,000

Which of the following is true about one-tailed and two-tailed tests?

A) For standard normal and t-distributions, which have a mean of zero, lower-tail

critical values are negative and upper-tail critical values are positive.

B) For an upper one-tailed test, if the test statistic is greater than the critical value, the

decision would be to fail to reject the null hypothesis.

C) For a lower one-tailed test, if the test statistic is less than the critical value, the

decision would be to fail to reject the null hypothesis.

D) For a two-tailed test, if the test statistic is either greater than the upper critical value

or less than the lower critical value, the decision would be to fail to reject the null

hypothesis.

The purpose of sampling is to ________.

A) enumerate all the values in the population

B) measure all items of interest for a particular interest or investigation

C) obtain sufficient information to draw a valid inference about a population

D) calculate all variables and observations within a population

Pickson Luthiers Corporation makes four models of electric guitars, ScarCT, Dela Mort,

Warax, and Invazen. Each guitar must flow through five departments, assembly,

painting, sound testing, inspection, and packaging. The table below shows the relevant

data. Production rates are shown in units/hour. (ScarCT is assembled elsewhere).

Pickson wants to determine how many guitars to make to maximize monthly profit.

According to the linear optimization model, what is the total number of ScarCTs

produced?

A) 2500

B) 750

C) 0

D) 100

Jonathan Reese is considering three stocks in which to invest with a fixed budget. The

table below provides information on Jonathan’s expected returns for each stock. The

table also provides information, collected from market researchers, on the

variance-covariance matrix of the individual stocks. He expects a total return of at least

10%.

Develop a quadratic optimization model to find the optimal allocation of the budget to

each stock, and variance calculations for squared terms and cross-products based on the

variance-covariance matrix.

According to the model, what is the cross-product value for Stock 1 variance?

A) 0.00176

B) 0.00450

C) -0.00047

D) 0.00194

Cerebro Manufacturing produces four types of structural support fittings-plugs, rails,

rivets, and clips-which are machined on two CNC machining centers. The machining

centers have a capacity of 250,000 minutes per year. The gross margin per unit and

machining requirements are shown in the spreadsheet below.

What is the total profit generated from the manufacture of only plugs?

A) $ 66,666.67

B) $ 100,000.00

C) $ 183,333.33

D) $ 150,000.00

Peige, a stock broker, has data consisting of price, price/earnings ratio, and market

capitalization for seven different stocks on one particular day. She wishes to plot these

three variables in two dimensions. Which of the following charts must Peige use?

A) Stock chart

B) Surface chart

C) Bubble chart

D) Line chart

Sujito Electronix makes headphones for $22 and sells them for $32. Sujito has sold at

least 50 headphones on average per week in the past, though the actual demand is

unknown. Sujito has also often run short of supply in the past. After three months of

release, the headphones are sold at 40 percent discount. The spreadsheet below shows

Sujito’s sales and demand for the headphones. We take demand at 51, and quantity

produced at 55.

Calculate the net profit for the headphones.

A) $586.8

B) $498.8

C) $1653.8

D) $466.8

How do test statistics for two-sample tests vary depending on whether the population

standard deviations are known, and if not, whether they are assumed to be equal?

While conducting regression analysis, how is constructing a normal probability plot

useful?

The table below is the data set of the Shiller Real Home Price Index for the years

1946-1956.

Setting k = 3, determine the value of root mean square of errors.

Find the range of volumes at which it is more economical for Nib ‘N’ Ink to produce the

refills in-house or outsource them. (Hint: Use the break-even decision model).

Blue Sunset Band is planning to record a new album. A major decision to be made is if

the band can record the album on their own, or if they should hire a studio to record it

with. The fixed cost for recording at the studio is $ 100,000, plus the manufacturing

cost per CD, which is at $5. If they record the album in- house, the cost per CD is $10.

They plan to produce 3000 copies of the album regardless of the place of recording. If

the band wished to break even with the cost, how can they achieve this by using the

Goal Seek feature in Excel?

What is a job-sequencing problem? How can we find an optimal solution for such

problems?