N = 5		Optimization Results								Allocation Results
\(\alpha\)		\(a\)	\(p_1\)	\(p_2\)	\(p_3\)	\(q_1\)	\(q_2\)	\(q_3\)		Group 1	Group 2	Group 3
0.1		5.2608	0.0913	0.1961	0.3023	0.9232	0.9747	1.0000		12.73%	31.03%	56.25%
0.2		6.3701	0.1023	0.2270	0.3719	0.9584	0.9846	1.0000		11.89%	31.82%	56.29%
0.3		6.9498	0.1085	0.2542	0.4375	0.9589	0.9889	1.0000		10.17%	31.13%	58.70%
0.4		7.4627	0.1162	0.2820	0.5087	0.9773	0.9912	1.0000		10.53%	30.72%	58.75%
0.5		7.7758	0.1226	0.3114	0.5868	0.9810	0.9927	1.0000		10.53%	30.65%	58.82%
0.6		8.0124	0.1290	0.3429	0.6720	0.9835	0.9936	1.0000		10.59%	29.23%	60.18%
0.7		8.2992	0.1356	0.3766	0.7639	0.9855	0.9943	1.0000		10.58%	29.21%	60.22%
0.8		8.5196	0.1425	0.4126	0.8607	0.9871	0.9948	1.0000		10.57%	29.19%	60.24%
0.9		8.6959	0.1495	0.4507	0.9606	0.9884	0.9952	1.0000		10.56%	29.17%	60.27%
1.0		8.8415	0.1569	0.4909	1.0617	0.9894	0.9955	1.0000		10.55%	29.16%	60.29%
1.1		8.9645	0.1646	0.5327	1.1617	0.9903	0.9957	1.0000		9.71%	28.19%	62.10%
1.2		9.1344	0.1725	0.5759	1.2592	0.9909	0.9960	1.0000		9.68%	30.09%	60.23%
1.3		9.2885	0.1807	0.6200	1.3527	0.9915	0.9962	1.0000		9.67%	30.06%	60.27%
1.4		9.4235	0.1892	0.6647	1.4412	0.9920	0.9964	1.0000		9.66%	30.04%	60.30%
1.5		9.5434	0.1980	0.7096	1.5242	0.9924	0.9965	1.0000		9.66%	30.01%	60.33%
1.6		9.6511	0.2071	0.7541	1.6015	0.9928	0.9967	1.0000		9.65%	29.99%	60.35%
1.7		9.7489	0.2165	0.7981	1.6731	0.9931	0.9968	1.0000		9.65%	29.97%	60.38%
1.8		9.8384	0.2261	0.8411	1.7392	0.9934	0.9969	1.0000		9.64%	29.96%	60.40%
1.9		9.9211	0.2360	0.8829	1.8001	0.9937	0.9970	1.0000		9.64%	29.94%	60.42%
2.0		10.0048	0.2461	0.9233	1.8563	0.9939	0.9971	1.0000		9.06%	28.94%	62.00%
N = 100		Optimization Results								Allocation Results
\(\alpha\)		\(a\)	\(p_1\)	\(p_2\)	\(p_3\)	\(q_1\)	\(q_2\)	\(q_3\)		Group 1	Group 2	Group 3
0.1		62.2839	0.0934	0.2057	0.3272	0.9294	0.9831	1.0000		14.31%	32.53%	53.17%
0.2		67.7119	0.1037	0.2332	0.3861	0.9644	0.9914	1.0000		14.27%	32.26%	53.46%
0.3		70.5103	0.1106	0.2587	0.4480	0.9750	0.9941	1.0000		14.09%	32.13%	53.78%
0.4		72.3996	0.1171	0.2854	0.5169	0.9818	0.9955	1.0000		14.10%	32.04%	53.86%
0.5		73.7877	0.1233	0.3142	0.5936	0.9853	0.9964	1.0000		13.84%	31.84%	54.32%
0.6		74.9113	0.1297	0.3453	0.6780	0.9876	0.9969	1.0000		13.90%	31.87%	54.24%
0.7		75.8366	0.1362	0.3788	0.7691	0.9893	0.9973	1.0000		13.69%	31.71%	54.60%
0.8		76.6451	0.1430	0.4145	0.8654	0.9905	0.9976	1.0000		13.83%	31.80%	54.37%
0.9		77.3476	0.1500	0.4525	0.9649	0.9915	0.9978	1.0000		13.75%	31.74%	54.50%
1.0		77.9538	0.1573	0.4925	1.0656	0.9923	0.9980	1.0000		13.67%	31.68%	54.64%
1.1		78.5252	0.1650	0.5342	1.1655	0.9929	0.9982	1.0000		13.67%	31.68%	54.65%
1.2		79.0247	0.1729	0.5773	1.2627	0.9935	0.9983	1.0000		13.59%	31.62%	54.79%
1.3		79.5024	0.1811	0.6214	1.3559	0.9940	0.9984	1.0000		13.59%	31.62%	54.79%
1.4		79.9183	0.1896	0.6660	1.4442	0.9943	0.9985	1.0000		13.40%	31.48%	55.12%
1.5		80.3390	0.1983	0.7108	1.5271	0.9947	0.9986	1.0000		13.50%	31.55%	54.94%
1.6		80.7121	0.2074	0.7553	1.6042	0.9950	0.9987	1.0000		13.50%	31.55%	54.95%
1.7		81.0645	0.2168	0.7991	1.6757	0.9953	0.9987	1.0000		13.42%	31.49%	55.09%
1.8		81.4104	0.2264	0.8421	1.7417	0.9955	0.9988	1.0000		13.42%	31.49%	55.10%
1.9		81.7244	0.2363	0.8838	1.8026	0.9957	0.9988	1.0000		13.41%	31.48%	55.11%
2.0		82.0221	0.2464	0.9242	1.8586	0.9959	0.9989	1.0000		13.33%	31.42%	55.25%