showing competence in analyzing a real-world decision-making situation using sophisticated mathematical models

RevolutionX is a startup tech company in robotics. The management is considering three different configurations for their new model, RobX. The three configurations are Prime, Limited, and Ultimate. The data for each of the configurations (per unit) is given in the following table. RevolutionX needs to find the optimal production of each of the configurations to maximize total profit.
  
Configuration

Profit ($)

Funding Needed ($)

Assembly (hrs)

Material (units)
 
Prime

1500

4500

45

32
 
Limited

2100

5300

61

41
 
Ultimate

3200

7100

83

63
Based on the marketing data the production of the Ultimate configuration cannot exceed the production of Prime and Limited configurations combined. Furthermore, the production of Prime and Limited configurations must be equal. 
The available funding could be 1, 2, 3, or 4 million dollars with the corresponding probabilities and . The chance of having 1 or 2 or 3 million dollars funding are equal (i.e., ). The chance of having 4 million dollars funding is double the chance of having 1 million dollars funding (i.e., ).
Currently they are considering three potential locations for their new factory that would be used to produce the new model. The three alternatives are: Boston, Chicago, and Huston. They need to choose one of these locations. The available Assembly hours and Material units depend on the location of the factory according to the following table:
   
Location

Assembly (hrs)

Material (units)
 
Boston

35000

15000
 
Chicago

30000

20000
 
Huston

25000

25000
A final constraint is that the production of the three configurations combined must be at least equal to the expected demand for the next month (i.e., May in the following table), that should be estimated using the following demand data for the past year.
  
Apr

May

June

July

Aug

Sept

Oct

Nov

Dec

Jan

Feb

Mar

Apr

May
 
3850

78

89

82

112

106

131

125

145

173

182

169

195

???
You need to answer the following questions based on quantitative analysis. You need to use Regression Analysis, Linear Programming, and Payoff Table Analysis to answer the following questions.
Question 1: What is the expected demand for May? If you get a fractional value for the May demand, you need to round it up or down and justify why you decided to round it up or down.
Question 2: Is the relationship between the month and demand strong? You need to answer this question using the appropriate quantitative measure from your model.
Question 3: Create the payoff table using the three locations as alternatives and the four available funding possibilities as scenarios. You need to calculate the payoff corresponding to each combination of location and funding scenario.
Question 4: What are the probabilities for funding scenarios (i.e., )? You need to show your calculation.
Question 5: What location should RevolutionX choose based on the expected profit for each location?
Question 6: What is the corresponding EVPI?
Question 7: Justify the value of EVPI. You need to provide a valid argument why EVPI has this particular value.
Question 8: What is the most important parameter(s) of the model to conduct sensitivity analysis on? You need to provide reasoning why you chose that parameter(s). Conduct sensitivity analysis on the parameter you believe is the most important one.
Note: You need to submit ONE WORD file and ONE EXCEL file. You need to answer ALL of the above questions in the WORD DOCUMENT based on your calculations in the EXCEL file.