Suppose you have a system of two masses strung over a pulley. Mass 1 (6.2 kg) hangs on the right side of the pulley suspended over the ground at height 0.7 m. Mass 2 (2.3 kg) hangs over the left side of the pulley and rests on the ground. The pulley is a uniform disk of mass m and radius 12.5 cm. When the system is released, Mass 1 moves down and Mass 2 moves up, such that Mass 1 strikes the ground with speed 0.7 m/s. This is called an Atwood Machine. Calculate the mass of the pulley in kg.

Use the table for the question(s) below . Consider the following expected returns, volatilities, and correlations: Stock Expected Return Standard Deviation Correlation with Duke Energy Correlation with Microsoft Correlation with Wal Mart − Duke Energy 14% 6% 1.0 1.0 − 0.0 Microsoft 44% 24% 1.0 − 1.0 0.7 Wal Mart − 23% 14% 0.0 0.7 1.0 Which of the following combinations of two stocks would give you the biggest reduction in risk? A. Microsoft and Duke Energy B. Duke Energy and Wal Mart − C. Wal Mart and Microsoft − D. No combination will reduce risk.

Consider the following time series data.

(a)

(b)

Develop the three-week moving average forecasts for this time series. (Round your answers to two decimal places.)

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7?

(c)

Use α = 0.2 to compute the exponential smoothing forecasts for the time series.

Compute MSE. (Round your answer to two decimal places.)

MSE =

What is the forecast for week 7? (Round your answer to two decimal places.)

(d)

Compare the three-week moving average approach with the exponential smoothing approach using

α = 0.2.

Which appears to provide more accurate forecasts based on MSE? Explain.

The three-week moving average provides a better forecast since it has a larger MSE than the smoothing approach.The exponential smoothing using α = 0.2 provides a better forecast since it has a larger MSE than the three-week moving average approach.     The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the three-week moving average approach.The three-week moving average provides a better forecast since it has a smaller MSE than the smoothing approach.

(e)

Use a smoothing constant of α = 0.4 to compute the exponential smoothing forecasts.

Does a smoothing constant of 0.2 or 0.4 appear to provide more accurate forecasts based on MSE? Explain.

The exponential smoothing using α = 0.4 provides a better forecast since it has a larger MSE than the exponential smoothing using α = 0.2.The exponential smoothing using α = 0.2 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.4.     The exponential smoothing using α = 0.4 provides a better forecast since it has a smaller MSE than the exponential smoothing using α = 0.2.The exponential smoothing using α = 0.2 provides a better forecast since it has a larger MSE than the exponential smoothing using α = 0.4.

The Mountain Red Vineyard (MRV) is planning to launch a luxury wine brand, MRV Shiraz to be sold at the fixed price ? = ? per barrel. The MRV operations research analyst conducted the

survey of MRV customers and obtained the discrete probability distribution of annual demand for the new luxury wine brand as shown in the table below.

(?)

Further the analyst developed the risk analysis simulation scenario assuming the MRV Shiraz sold quantity is a random variable with discrete probability distribution shown in the table below.

0

3

(?)

The risk analysis simulation scenario also included the fixed cost ? = $300 per barrel of the MRV Shiraz. This cost is associated with introduction and operation of the new production line.

The MRV is committed to have enough supply to meet the demand. The profit function is ? = ? × ? − ? × ?.

Name the Excel sheet ‘Problem 3’.

enter ? = ? of your choice into the cell $B$4;0

Set the input parameter values:

figure below.

0

enter ? = $300 into the cell $B$5.
Your implementation of the simulation model should also include the information shown in the

Let N be the sample size.

1) Could we use a single standard uniform random variable (e.g. to be generated in column B) for simulation of ‘Demand’ and ‘Sold’ quantities instead of two standard uniform random variables? Provide your reasoning.

2) Let ? = 50. Report the average profit and standard deviation of the profit. Construct a 95% - confidence interval for the expected profit using your simulation results.

3) Let ? = 500. Report the average profit and standard deviation of the profit. Construct a 95% - confidence interval for the expected profit using your simulation results.

4) Comment on the tendency of the 95% - confidence intervals obtained in 2) and 3). Explain your answer.

4

5) Give a ‘break-even’ price estimate, you would recommend to the MRV operations research analyst, using your simulation results. Give your reasoning.

Scenario: Imagine you are a researcher who is interested in studying whether sleep deprivation leads to increased reaction times (i.e., being slower) when driving. You randomly select a sample of 30 licensed drivers. Fifteen participants are randomly assigned to get 5 hours of sleep for three consecutive nights. The other 15 participants are randomly assigned to get 8 hours of sleep for three consecutive nights. For the purposes of this Assignment, assume that all participants sleep exactly the required amounts. After the third night, all participants take a driving simulation test that measures their reaction times.

Use SPSS to determine if amount of sleep is related to reaction time.

1. Explain whether the researcher should use an independent-samples t-test or a related-samples t-test for this scenario. Provide a rationale for your decision.
2. Identify the independent variable and dependent variable.
3. Knowing the researcher believes that people who sleep less will have slower reaction times, state the null hypothesis and alternate hypothesis in words (not formulas).
4. Explain whether the researcher should use a one-tailed test or two-tailed test and why.
5. Identify the obtained t value for this data set using SPSS and report it in your answer document.
6. State the degrees of freedom and explain how you calculated it by hand.
7. Identify the p value using SPSS and report it in your answer document.
8. Explain whether the researcher should retain or reject the null hypothesis. Provide a rationale for your decision. Are the results statistically significant?
9. Explain what the researcher can conclude about the relationship between amount of sleep and reaction times.

Data:

Reaction times in seconds for participants with 5 hours of sleep
0.22
0.25
0.27
0.25
0.24
0.28
0.24
0.3
0.25
0.21
0.28
0.23
0.29
0.25
0.29

Reaction times in seconds for participants with 8 hours of sleep
0.21
0.23
0.2
0.24
0.28
0.23
0.3
0.29
0.23
0.21
0.21
0.27
0.29
0.23
0.25

1. A small mattress company recently started its operations and currently does not have enough resources to utilize high-tech forecasting software. The manager wants to utilize traditional methods of forecasting to estimate demand. The following recent data on monthly sales are available from the past year. Use this information to answer the following set of questions.

1. If the manager uses a naïve forecasting method. What is the forecast for Jan 2020? (2 pts.)

1. Use the three-period moving average method and estimate forecast beginning from Aug-19 to Jan-20. Use 0.4, 0.3, and 0.2 as weights with highest weights given to the most recent periods (8 pts.)
   
2. Calculate the Mean Absolute Deviation of forecasts from the three-period moving average. (5 pts.)
   

              2. Use the same date from Q1. to answer the following questions. (10 pts.)

1. Use the exponential smoothing method to calculate forecast from Aug-19 to Jan-20. Use an α value of 0.3.

You need a beginning forecast of Jul-19 to start this. Use the naïve forecast for estimating Jul-19, and then use the answer to start the exponential smoothing method.

(Please show all the work for credit on this. You can use excel too, but show the logic/formula if using excel)

**Government activities may be less “profitable” than they appear**

A city prepares its budget in traditional format, classifying expenditures by fund and object. In 2010, amid considerable controversy, the city authorized the sale of $20 million in bonds to finance construction of a new sports and special events arena. Critics charged that, contrary to the predictions of arena proponents, the arena could not be fiscally self‐sustaining. Five years later, the arena was completed and began to be used. After its first year of operations, its general managers submitted the following condensed statement of revenues and expenses (in millions):

At the city council meeting, when the report was submitted, the council member who had championed the center glowingly boasted that his prophecy was proving correct; the arena was “profitable.” Assume that the following information came to your attention:

• The arena is accounted for in a separate enterprise fund.

• The arena increased the number of overnight visitors to the city. City administrators and economists calculated that the additional visitors generated approximately $0.1 million in hotel occupancy tax revenues. These taxes are dedicated to promoting tourism in the city. In addition, they estimated that the ticket and concession sales, plus the economic activity generated by the arena, increased general sales tax revenues by $0.4 million.

• The city had to improve roads, highways, and utilities in the area surrounding the arena. These improvements, which cost $6 million, were financed with general obligation debt (not reported in the enterprise fund). Principal and interest on the debt, paid out of general funds, were $0.5 million. The cost of maintaining the facilities was approximately $0.1 million.

• On evenings when events were held in the arena, the city had to increase police protection in the arena’s neighborhood. Whereas the arena compensated the police department for police officers who served within the arena itself, those who patrolled outside were paid out of police department funds. The police department estimated its additional costs at $0.1 million.

• The city provided various administrative services (including legal, accounting, and personnel) to the arena at no charge at an estimated cost of $0.1 million.

• The city estimates the cost of additional sanitation, fire, and medical services due to events at the center to be approximately $0.2 million.

1. Would you agree with the council member that the arena was fiscally self‐sustaining?

2. In which funds would the additional revenues and expenditures be budgeted and accounted for?

3. Comment on the limitations of both the traditional object classification budget and fund accounting system in assessing the economic costs and benefits of a project—such as the sports and special events arena.

4. What changes in the city’s budgeting and accounting structure would overcome these limitations? What additional problems might these changes cause?

assume that a dam cost 17 million to build in a year and that beginning in the next year, the dam yields net benefits of 2 million per year for 10 years. If the discount rate is equal to 7 percent, what is the net present value of the dam? should it be built or not? What happens if the chosen discount rate is 2%? should the dam built, now?

Two point particles separated by 0.8 m carry a total charge of 185