Refer to the clustering problem involving the file FBS described in Problem 1. The NCAA has a preference for conferences consisting of similar schools with respect to their endowment, enrollment, and football stadium capacity, but these conferences must be in the same geographic region to reduce traveling costs. Follow the following steps to address this desire. Apply k-means clustering using latitude and longitude as variables with k 5 3. Be sure to Normalize Input Data and specify 50 iterations and 10 random starts in Step 2 of the XLMiner k-Means Clustering procedure. Using the cluster assignments, separate the original data in the Data worksheet into three separate data sets one data set for each of the three regional clusters. a. For Region 1 data set, apply hierarchical clustering with Wards method to form four clusters using football stadium capacity, endowment, and enrollment as variables. Be sure to Normalize Input Data in Step 2 of the XLMiner Hierarchical Clustering procedure. Using a PivotTable on the data in the corresponding HC_Clusters worksheet, report the characteristics of each cluster. b. For the Region 2 data set, apply hierarchical clustering with Wards method to form three clusters using football stadium capacity, endowment, and enrollment as variables. Be sure to Normalize Input Data in Step 2 of the XLMiner Hierarchical Clustering procedure. Using a PivotTable on the data in the corresponding HC_ Clusters worksheet, report the characteristics of each cluster. c. For the Region 3 data set, apply hierarchical clustering with Wards method to form two clusters using football stadium capacity, endowment, and enrollment as variables. Be sure to Normalize Input Data in Step 2 of the XLMiner Hierarchical Clustering procedure. Using a PivotTable on the data in the corresponding HC_ Clusters worksheet, report the characteristics of each cluster. d. What problems do you see with the plan with defining the school membership of nine conferences directly with the nine total clusters formed from the regions? How could this approach be tweaked to solve this problem