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QuantMethods Productions Operations Management Software

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Please reference the attachment and respond to questions 1, 2, 3, 4 & 5 on page 137, questions 1, 2, & 3 on page 269, and question 10 on page 271. For your convenience, the assigned questions are circled. Questions involve cost of quality, shape and position, minimum total cost, scatter diagram, electronic components, and control operations.

Please include all work along with the answer including formulas.

Measurable data, independent and dependent variables

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Research wireless cell phone using systematic sampling for its simplicity: Any individuals of any age who is a customer with a data plan under various cellular phone carriers will be randomly selected from the lists acquired from these cell phone carriers. The population to be analyzed is 2,000 cell phone users, and a sample of 500 is selected. Starting with the 2nd person on the list, every 4th person will be given the survey.

Question:

What will be measurable data in this case and (assume a survey will be conducted and or data can be obtain)? What will be at least two independent variables and one dependent variable (assuming they are consistent with the collected data)?

Internal and external validity

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I don’t understand what internal and external threats are and could you provide some examples of what would be considered a threat to internal and/or external validity of a study design.

Manufacturer level of significance, least squares regression line

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Please choose the correct answer and write briefly why:

A manufacturer of a chemical used in glue, attempting to control the amount of a hazardous chemical its workers are exposed to, has given instructions to halt production if the mean amount in the air exceeds 3.0ppm. It is believed that the standard deviation is 0.5. ppm from a previous study. A random sample of 50 air specimens produced the sample mean=3.1 ppm. If the significance level of shutting down production is set at α = 0.05, given this air sample should production be halted?

a. No
b. Yes
c. Insufficient information to make a decision
d. Depends on the power of the Test

The least squares regression line minimizes the sum of the:
a. Differences between actual and predicted Y values
b. Absolute deviations between actual and predicted Y values
c. Absolute deviations between actual and predicted X values
d. Squared differences between actual and predicted Y values
e. Squared differences between actual and predicted X values

Analyzing Revenue: Scatter Diagram, Variation in Revenue

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A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income an number of rooms occupied.
(Please see the attached file)

Use a statistical software package to answer the following questions.
a) Does the breakfast revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.
b) Determine the coefficient of correlation between the two variables. Interpret the value.
c) Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level.
d) What percent of the Variation in revenue in the restaurant is accounted for by the number of rooms occupied?

Autocorrelation and heteroscedasticity

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Open the Cons Trans 59 – 00.xls file. Use the BEA consumption and transfers data to investigate whether heteroscedasticity or autocorrelation is present in the model using the graphical approach (consumption as the dependent variable). Which answer best represents the degree of autocorrelation in the model? Using EXCEL or PHStat2, answer the following:

a) Neither autocorrelation nor heteroscedasticity appear to be present in the model.
b) Autocorrelation appears to be present in the model.
c) Heteroscedasticity appears to be present in the model.
d) Both autocorrelation and heteroscedasticity appear to be present in the model

Refer to the BEA consumption and transfers data from the Cons_Trans_59-00.xls file which was used in Problem 1, above. Analyze the signs of the residuals and values of the residuals to determine which best describes the pattern in the residuals

a) The signs of the residuals are randomly arranged and the values of the residuals remain constant.
b) The signs of the residuals reveal a non-random pattern and the values of the residuals remain constant.
c) The signs of the residuals reveal a non-random pattern and the values of the residuals increase as the transfers increase.
d) The signs reveal are randomly arranged and the values of the residuals increase as the transfers increase.

Use the Cons Trans 59-00.xls file, which was, used in Problems 1 & 2 and PHStat2, Excel, or other means to calculate the d statistic. The calculated d-statistic is:

a) 0.635267892
b) 1.355377418
c) 0.877545537
d) 0.355377418

The dl and du at a 0.01 level of significance in the Durbin-Watson test for autocorrelation are:

a) 1.44 & 1.54, respectively.
b) 1.48 & 1.57, respectively.
c) 1.25 & 1.34, respectively.
d) 1.24 & 1.42, respectively.

Use the results of the Durbin-Watson test in Problems 3 & 4 to determine if autocorrelation exists in the model. Test at the 0.01 level of significance. The statistical conclusion is:

a) No evidence of autocorrelation.
b) No conclusion can be drawn.
c) Autocorrelation exists in the model.
d) Not enough information to determine if autocorrelation exists.

Sandford Tile Case Study: Linear Optimization Problem

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Sandford Tile company makes ceramic and porcelain tile for residentail and commercial use. They produce three different grades of tile for walls, residential flooring, and commercial flooring each of which requires different amounts of materials and production time and generates different contribution to profit. The spreadsheet shows the percentage of materials needed for each grade and the profit per square foot. Each week Sandford tile receives raaw materials shipments and the operations manager must schedule the plan to efficiently use the matierals to maximize profitability. Currently inventory consists of 6000 pounds of clay, 3000 pounds of silica, 5000 pounds of sand, and 8000 pounds of Feldspar. Because demand varies for the different grades marketing estimates that at most 8000 square feet of grade III tile should be produced and that at east 1500 square feet of grade i tiles are required. Each square foot of tile weighs two pounds.
1. Develop a linear optimization model to determine how many of each grade of tile the company should make next week to maximize profit.
2. Implement the model on a spreadsheet and find an optimal solution
3. Explain the sensitivity information for the objective soefficients. What happens in the projit on Grade I is increased by $.05?
4. If an additional 500 pounds of feldspar is available how will the optimal solution be affected?
5. 1,000 pounds of clay are found to be of poor quality, what should the company do?
6. Use the auxilary variable cells technique to handle the bound contraints and generate all shadow prices.