GP 249 Midterm | Course Paper

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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%

Letherin Hides is a company that makes boots specifically targeting college students.

Forecasts of sales for the next year are 200 in the summer, 450 in the autumn, and 500

in the winter. Accessories that are used on the boots are purchased from a supplier for

$31.66. The cost of capital is estimated to be 24% per year (or 6% per quarter); thus, the

holding cost per item is 0.06($31.66) = $1.9 per quarter (rounded figure). Letherin

Hides hires freelance art designers at part-time to craft designs during the summer, and

they earn $ 6 per hour. In the autumn, labor is more difficult to keep, and the owner

must pay $6.5 per hour to retain qualified help. Because of the high demand for

part-time help during the winter holiday season, labor rates are higher in the winter, and

workers earn $7.75 per hour. Each boot design takes 2 hours to complete. How should

production be planned over the three quarters to minimize the combined production and

inventory holding costs?

The table below provides information on Letherin Hides boot design cost and

production.

According to the linear optimization model, what is the total cost incurred by Letherin

Hides for the combined seasons?

A) $17,885

B) $15,605

C) $15,700

D) $18,700

Using an empirical distribution precludes sampling values outside the range of the

actual data.

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 Testing cell?

A) 7.00

B) 17.50

C) 22.50

D) 27.50

The means of all possible samples of a fixed size n from some population will form a

distribution which is known as the ________.

A) corollary of the mean

B) sampling distribution of the mean

C) standard error of the mean

D) point estimate

What is the mean absolute deviation obtained from the simulation results?

A) 39.10

B) 24.56

C) 58.75

D) 46.36

For an independent variable Y, the error associated with the ith observation is:

A) ei = Yi – Å¶i

B) Yi = (ei)2 – Å¶i

C) (Å¶i)2 ei = Yi

D) ei = (Yi + Å¶i)2

The details of the clock sales at a supermarket for the past 6 weeks are shown in the

table below. The time series appears to be relatively stable, without trend, seasonal, or

cyclical effects. The simple moving average value of k is set at 2.

Using the data, determine the value of the simple moving average root mean square

error.

A) 0.21

B) 14.39

C) 20.12

D) 207.13

Which of the following is true about chi-square distribution?

A) It is a special distribution and is denoted by (C2).

B) It is characterized by degrees of freedom.

C) It is computed using the Excel function CHISQ.INV.TEST.

D) It has a left-tail area equal to the expected value of the sample.

Following is an extract from the Cost per Order Database of Grogtes LLC.

Which of the following does the second quartile of the costs per order indicate?

A) 2% of the costs per order are less than or equal to $114.84.

B) 20% of the costs per order are less than or equal to $1,200.12.

C) 5% of the costs per order are less than or equal to $229.36.

D) 50% of the costs per order are less than or equal to $286.16.

The Risk Solver Platform ________ feature allows you to determine the influence that

each uncertain model input has individually on an output variable based on its

correlation with the output variable.

A) trend chart

B) sensitivity chart

C) overlay chart

D) box-whisker chart

The strength of the association rule, known as lift, is calculated as the ratio of the

________.

A) sum of the antecedents and the consequents to the antecedents

B) antecedents to the consequents

C) support to the confidence level

D) confidence to expected confidence

Which of the following distributions is appropriate when the probability of zero is very

low, but the most likely value is just greater than zero?

A) triangular distribution

B) exponential distribution

C) lognormal distribution

D) beta distribution

Below is the table showing rate of shoes sold per day and the highest-priced shoe sold

that day for a one-week period. The rate of shoes sold per day (X) and the price of the

shoes (Y).

Use Excel to calculate the z-score of X observation 27.

A) -0.24

B) 0

C) 0.18

D) 1.46

The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues.

They have three classes of tickets: Classic, Silver, and Gold. The table below provides

information on the average ticket sales, revenue and price elasticity on demand. They

have a total seating capacity of 300. The table also provides the price range within

which they plan to reduce their ticket rates.

According to the nonlinear model, what is the new price for Classic tickets?

A) $7.50

B) $12.45

C) $6.50

D) $8.20

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

surfboards, the Rockwell and the Limestone models. The manufacturing process

consists of two departments: fabrication and finishing. The fabrication department has

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

5 workers, who also work a 5-hour shift. Each pair of Rockwell surfboards requires 3

labor hours in the fabrication department and 1.5 labor hours in finishing. The

Limestone model requires 4.5 labor- hours in fabrication and 2 labor-hours in finishing.

The company operates 6 days a week. It makes a per-unit profit of $60 on the Rockwell

model and $75 on the Limestone model. Approximately 4.1 Rockwell models and 8.4

Limestone models are produced per day.

What is the total number of hours used for the finishing operation?

A) 42.58

B) 50.10

C) 35.64

D) 22.95

Belowisaspreadsheetofpurchaseordersfor acomputerhardwareretailer.

For which of the following columns can the COUNT function be performed?

A) column G

B) column E

C) column B

D) column A

Below is a room overbooking model spreadsheet for the Metza, a hotel chain. The hotel

has 425 rooms priced at $180 per day each, and is usually fully booked. Reservations

can be cancelled any time before 5:00 p.m. with no penalty. The hotel estimates an

average overbooking cost of $150. Customer demand is set at 400 with an average

cancellation of 20.

Calculate the customer arrivals at the Metza.

A) 425

B) 405

C) 400

D) 380

A ________ is a range of values between which the value of the population parameter is

believed to be, along with a probability that the interval correctly estimates the true

population parameter.

A) point estimate

B) frequentist interference

C) confidence interval

D) fiducial inference

Below is the spreadsheet for a portfolio allocation model.

Answer the following question(s) using a model with uncertainty on type of investment

return. Assume that the distributions of life insurance annual return is uniform with

minimum 4% and maximum 6%, bond mutual funds annual return is normal with mean

7% and standard deviation 1%, stock mutual funds annual return is lognormal with

mean 11% and standard deviation 4%. Use 10,000 trials and 1 for random seed for the

simulation.

What is the mean absolute deviation obtained from the simulation results for

maximizing the total expected return? [Hint: Choose the approximate value.]

A) $ 887.25

B) $ 735.86

C) $ 651.97

D) $ 967.36

The Riviera Transport Company (RTC) produces car accessories at two plants: Dallas

and Atlanta. They ship them to major distribution centers in Houston, San Jose,

Jacksonville, and Memphis. The accounting, production, and marketing departments

have provided the information in the table below, which shows the unit cost of shipping

between any plant and distribution center, plant capacities over the next planning

period, and distribution center demands. RTC’s supply chain manager faces the problem

of determining how much to ship between each plant and distribution center to

minimize the total transportation cost, not exceed available capacity, and meet customer

demand.

Assume Xij = amount shipped from plant i to distribution center j, where i = 1

represents Dallas, i = 2 represents Atlanta, j = 1 represents Houston, and so on.

Which of the following is the objective function for cost minimization?

A) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 / 10.75 X21 +15.16

X22 +9.65 X23 +18.5 X24

B) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 + 10.75 X21 +15.16

X22 +9.65 X23 +18.5 X24

C) minimize cost = 13 X11 +15.25 X12 +10.99 X13 +18.48 X14 – 10.75 X21 +15.16

X22 +9.65 X23 +18.5 X24

D) minimize cost = (13 X11 +15.25 X12 +10.99 X13 +18.48 X14 – 10.75 X21 +15.16

X22 +9.65 X23 +18.5 X24 )(1,250 / 750)

Which of the following probabilities gives the confidence coefficient?

A) P(rejecting H0 | H0 is true)

B) P(not rejecting H0 | H0 is false)

C) P(rejecting H0 | H0 is false)

D) P(not rejecting H0 | H0 is true)

Below is a room overbooking model spreadsheet for the Metza, a hotel chain. The hotel

has 425 rooms priced at $180 per day each, and is usually fully booked. Reservations

can be cancelled any time before 5:00 p.m. with no penalty. The hotel estimates an

average overbooking cost of $150. Customer demand is set at 400 with an average

cancellation of 20.

Calculate the customer arrivals at the Metza.

A) 425

B) 405

C) 400

D) 380

____is a logical function that returns one value if the condition is true and another if the

condition is false

A) OR(condition 1, condition 2’¦)

B) AND(condition 1, condition 2’¦)

C) TO(value if true, value if false)

D) IF(condition, value if true, value if false)

Which of the following features of classification, used in Excel, for a particular

database will necessarily be coded to a certain value?

A) categorical variables

B) non-numerical variables

C) predictor variables

D) numerical variables