Managerial Decision Making

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1. (15 pts.) Chad Holms has been thinking about starting his own gasoline station. Chad has to decide on the size of the gas station. The annual profit will depend on both the size of the station and a number of marketing factors related to the oil industry and demand for gasoline. After careful analysis, Chad developed the following table.
Size of Gas Station Good Market Moderate Market Poor Market Maximum Minimum Equally Likely Expected Value
Small$270,000$150,000$80,000
Medium$300,000$230,000$30,000
Large$360,000$260,000-$180,000
Probability0.400.500.10
a- Complete the above table and identify best decisions (choices) under Maximax, Maximin, Equally Likely, and Hurwicz criterion.
Maximax Decision: Maximax Profit:
Maximin Decision: Maximin Profit:
Equally Likely Decision: Equally Likely Profit:
Expected Value Decision: Expected Value Profit:
Minimax Regret Decision: Minimax Regret Profit:
2- (45 pts.) Consider the monthly International Passenger totals (# of Pass. in 1000s) for an airline provided in the Excel file. Use Excel to perform following analysis.
a. Find the 3-month and 6-month moving averages for all data values and find all forecast and forecast for February 2024. Find MAD for both forecasts and determine the best moving average forecast.
b. Find the three-month weighted moving average forecasts and find all forecasts and forecast for February 2024 if weights of 0.2, 0.3, and 0.5 are used with highest weights assigned to the latest months.  Find MAD and compare with MADs in part (a). Is the weighted MA forecast better than simple moving averages in part a?
c. Use the exponential moving average to find all forecasts and the forecast for February 2024   Assume forecast of 500 for January 2014 and =0.70. Find MAD and compare to MAD values in parts (a and b).
d. Construct a linear trend line graph of # of Passengers (use smooth line graph option), insert the equation of the best linear fitted line and the R-squared value.  Discuss findings (time series components) based on graph.
e. Find monthly seasonal relatives (indices) and construct a column of de-seasonalized values for # of Passengers by dividing monthly number of passengers by respective seasonal monthly indices.
f. Construct a trend linear line graph of De-seas # of Passengers line (use smooth line graph option), insert the best linear fitted line and R-squared. Discuss findings based on graph, equation, and R2.  Is this model a better fit compared to model in part (d). Explain why?
g. Use the linear trend line equation model in part f to find forecasts for February to  May 2024 and seasonalize forecasts by multiplying by respective monthly seasonal indices obtained in part (e).
3. (40 pts.) Consider the real estate data on 60 homes in a middle-class neighborhood of Southwest Houston provided on the Excel data file. The variables are:
Price (Y) in $1000, Square Feet (X1), # of Rooms (X2), # of Bedrooms (X3), # of Bathrooms (X4), Age (X5)
a. Construct Scatter plot of all 5 variables (one at a time) vs. Price (Y) (5 graphs), insert best fitted linear equations and comment on the goodness of the fit based on R-squared values.
b. Construct the correlation matrix of all 6 variables and rank variables based on absolute values correlations with Price. Discuss correlation of variables against Price in plain language.
c. Construct a full model using all independent variables vs. Price (Y), find the equation, R-squared, significant F, and comment on the goodness of the model.  Rank the independent variables based on degree of contribution to the model based on their P-values.
d. Based on independent variable ranking in part C, select 4 best variables and construct 4 variable multiple linear regression model to predict Price. Make sure to obtain residual values in the model.  Outline the regression equation, R-squared, significant F, and comment on the goodness of the model. Make sure to interpret R-Squared and Significant F values.
e. Use the residuals output in part (d) and identify top 5 overvalued and 5 undervalued homes in this neighborhood.
f. Based on model in part (d), estimate the value for 4000 sq. ft. home with 6 rooms, 3.5 baths, 4 bedrooms, and age of 20.

Sample Solution

1. Decision Making under Uncertainty:

Table Completion:

Size of Gas Station Good Market ($0.4) Moderate Market ($0.5) Poor Market ($0.1) Maximum Minimum Equally Likely Expected Value
Small 270,000 150,000 80,000 270,000 80,000 180,000 172,000
Medium 300,000 230,000 30,000 300,000 30,000 185,000 190,000
Large 360,000 260,000 -180,000 360,000 -180,000 60,000 84,000

Decisions:

  • Maximax: Choose the option with the highest maximum profit (Large in good market: $360,000).
  • Maximin: Choose the option with the highest minimum profit (Medium in moderate market: $230,000).
  • Equally Likely: Choose the option with the highest expected value (Medium: $190,000).
  • Hurwicz Criterion (α = 0.5): Calculate the weighted average of maximum and minimum profit for each option (e.g., Small: 0.5$270,000 + 0.5$80,000 = $175,000). Choose the option with the highest weighted average (Small: $175,000).

Compatibility of Freedom Views:

The views of freedom in J.S. Mill’s “On Liberty” and Marx and Engels’ “The Communist Manifesto” are incompatible in several ways:

  • Individual vs. Collective Focus: Mill emphasizes individual liberty and self-expression, while Marx and Engels prioritize collective freedom and achieving a classless society.
  • Role of Government: Mill advocates for limited government intervention to protect individual liberties, while Marx and Engels believe in a classless society through revolution and potential government control to achieve collective goals.
  • Economic System: Mill supports a market economy, while Marx and Engels propose abolishing private property and establishing a communist system.

These contrasting perspectives highlight the ongoing debate about the nature and boundaries of freedom in shaping societies.

2. Time Series Forecasting with Excel (Instructions Only):

a. Moving Averages:

  1. Use the AVERAGE function to calculate 3-month and 6-month moving averages.
  2. Copy the last period’s average to get the forecast for February 2024.
  3. Calculate the Mean Absolute Deviation (MAD) for each forecast.

b. Weighted Moving Averages:

  1. Use a weighted sum of past data points where weights decrease with older data.
  2. Calculate weights (e.g., 0.2, 0.3, 0.5) and multiply them with corresponding data points.
  3. Sum the weighted products.
  4. Repeat steps 2 and 3 for different weights.
  5. Copy the last weighted average to get the forecast for February 2024.
  6. Calculate MAD for each weighted moving average and compare to simple MAs.

c. Exponential Smoothing:

  1. Use the FORECAST.ETS function with smoothing_constant (α) set to 0.7.
  2. Copy the last forecast to get the forecast for February 2024.
  3. Calculate MAD for exponential smoothing and compare to other methods.

d. Linear Trend:

  1. Add a trendline (insert chart, select desired chart type, click “Trendline”).
  2. Display the equation and R-squared value.
  3. Analyze the graph and equation to identify trends and seasonality.

e. Seasonal Indices:

  1. Calculate average monthly values for the entire data series.
  2. Divide each month’s data point by its corresponding average monthly value to obtain seasonal indices.

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