The file ClassificationData.xlsx

ClassificationData-3.xlsxDownload ClassificationData-3.xlsx

contains the following information about 25 MBA programs:

• percentage of applicants accepted,
• percentage of accepted applicants who enroll,
• mean GMAT score of enrollees,
• mean undergraduate GPA of enrollees,
• annual cost of school (for state schools, this is the cost for out-of-state students),
• percentage of students who are minorities,
• percentage of students who are non-U.S. residents, and
• mean starting salary of graduates (in thousands of dollars).

Use these data and the Evolutionary Solver to divide these schools into 4 clusters, by finding 4 schools to be used as cluster centers and assigning all other schools to one of these cluster centers such that the sum of the distances from each school to its cluster center is minimized. More precisely, Each school is then assigned to the nearest cluster center, where nearest is defined in terms of the eight attributes.

What are the 4 cluster centers minimizing the sum of the distances from each school to the nearest cluster center and what is the corresponding optimal value?

Hint: Your model will have four decision variables (changing cells) corresponding to the indexes of the four schools chosen as cluster centers. Thus your constraints would be 1<= centers <=25 and centers=Integer.

Then for each school i, you need to compute the distance between that school and each center. You can use SQRT(SUMXMY2(Data of school i, Data of center j)) for each school i and center j. Then take the minimum of the four values for each school. Your objective function would be the sum of these minimums.

In addition, note that you need to first standardize the value of each attribute by subtracting the attributes mean and dividing the difference by the attributes standard deviation.

below is the classification data

MBA program data
School	% accepted	% accepted who enroll	Mean GMAT	Mean GPA	Total Cost	% minority	% non-US	Mean Starting Salary
Wharton	15	71	662	3.42	32400	16	30	102
Michigan	28	44	645	3.3	29800	15	26	86
Northwestern	14	69	660	3.3	32600	9	24	99
Harvard	13	88	680	3.5	30100	19	27	114
Virginia	19	49	660	3.1	31200	20	12	93
Columbia	14	70	660	3.3	32200	12	24	93
Stanford	7	81	690	3.6	34500	25	25	111
Chicago	23	57	685	3.4	34200	5	23	90
MIT	14	12	650	3.5	36700	15	37	101
Dartmouth	14	49	669	3.39	32700	9	16	104
Duke	17	50	646	3.33	30100	12	19	84
UCLA	17	55	651	3.5	27100	10	20	91
Berkeley	13	51	652	3.42	29100	11	35	91
NYU	20	11	646	3.3	32700	8	35	79
Indiana	45	20	630	3.2	21000	8	16	68
Washington U	43	40	606	3.2	28000	6	39	62
Carnegie-Mellon	31	65	638	3.2	27200	2	38	86
Cornell	25	38	634	3.3	29600	11	28	55
UNC	19	55	630	3.3	17500	16	19	80
Texas	18	12	631	3.3	19100	14	17	69
Rochester	36	34	630	3.22	28200	9	46	68
Yale	23	54	676	3.38	32000	15	31	88
SMU	62	48	601	3	26300	5	22	63
Vanderbilt	42	47	615	3.2	29700	7	23	63
Thunderbird	75	64	572	3.41	23800	10	33	57