5 Assets
Returns:  10.9176 13.6357 15.84892 8.69405 8.3573
Var - Cov Matrix
367.843 264.69 292.1499 59.9763 21.718
264.69 349.275 345.3725 98.5251 45.6425
292.15 345.373 651.2748 29.2018 1.56749
59.9763 98.5251 29.20177 127.48 70.8837
21.718 45.6425 1.567486 70.8837 44.7809
A=H= mu1 mu2 mu3 mu4 mu5
1 1 1 1 1
Target Return: 9.1 AT mu1 1
mu2 1
mu3 1
mu4 1
mu5 1
Min: h1+h2
ST
Z x1 x2 x3 x4 x5 u1 u2 v1 v2 v3 v4 v5 h1 h2 RHS
Row Zero 1 1000 1000 0
n -equations -367.84 -264.69 -292.15 -59.976 -21.72 -10.918 -1 1 = 0
-264.69 -349.27 -345.37 -98.525 -45.64 -13.636 -1 1 = 0
-292.15 -345.37 -651.27 -29.202 -1.567 -15.849 -1 1 = 0
-59.976 -98.525 -29.202 -127.48 -70.88 -8.6941 -1 1 = 0
-21.718 -45.643 -1.5675 -70.884 -44.78 -8.3573 -1 1 = 0
2-Equations 10.918 13.636 15.849 8.694 8.357 1 = 9.1
1 1 1 1 1 1 = 1
New Row Zero 1 -11918 -14636 -16849 -9694.1 -9357 0 0 0 0 0 0 0 0 0 -10100
Z x1 x2 x3 x4 x5 u1 u2 v1 v2 v3 v4 v5 h1 h2 RHS
Tableau 1 Row zero 1 -11918 -14636 -16849 -9694.1 -9357 0 0 0 0 0 0 0 0 0 -10100 Ratio
x3 in; h1 out v1 0 -367.84 -264.69 -292.15 -59.976 -21.72 -10.918 -1 1 0 0 0 0 0 0 0
ignore neg coeff v2 0 -264.69 -349.27 -345.37 -98.525 -45.64 -13.636 -1 0 1 0 0 0 0 0 0
v3 0 -292.15 -345.37 -651.27 -29.202 -1.567 -15.849 -1 0 0 1 0 0 0 0 0
v4 0 -59.976 -98.525 -29.202 -127.48 -70.88 -8.6941 -1 0 0 0 1 0 0 0 0
v5 0 -21.718 -45.643 -1.5675 -70.884 -44.78 -8.3573 -1 0 0 0 0 1 0 0 0
h1 (x3) 0 10.9176 13.6357 15.8489 8.6941 8.357 0 0 0 0 0 0 0 1 0   9.1 0.574172
h2 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1
Tableau 2 Row zero 1 -311.15 -139.65 0 -451.44 -472.7 0 0 0 0 0 0 0 1063.1 0 -425.8 Ratio
x5 in; h2 out v1 0 -166.59 -13.338 0 100.28 132.3 -10.918 -1 1 0 0 0 0 18.433 0 167.7 1.672677
ignore neg coeff v2 0 -26.78 -52.132 0 90.932 136.5 -13.636 -1 0 1 0 0 0 21.792 0 198.3 2.180788
v3 0 156.482 214.954 0 328.06 341.9 -15.849 -1 0 0 1 0 0 41.093 0 373.9 1.139862
v4 0 -39.861 -73.401 0 -111.46 -55.49 -8.6941 -1 0 0 0 1 0 1.8425 0 16.77
v5 0 -20.638 -44.294 0 -70.024 -43.95 -8.3573 -1 0 0 0 0 1 0.0989 0 0.9
x3 0 0.68885 0.86035 1 0.5486 0.527 0 0 0 0 0 0 0 0.0631 0 0.574 1.046692
h2 (x5) 0 0.31115 0.13965 0 0.4514 0.473 0 0 0 0 0 0 0 -0.0631 1   0.426 0.943263
Z x1 x2 x3 x4 x5 u1 u2 v1 v2 v3 v4 v5 h1 h2 RHS
Tableau 3* Row zero 1 -2E-12 -1E-12 0 0 0 0 0 0 0 0 0 0 1000 1000 -2E-12 Ratio
u1 in; v3 out v1 0 -253.7 -52.434 0 -26.102 0 -10.918 -1 1 0 0 0 0 36.098 -280 48.53
Remove complementary Slackness v2 0 -116.61 -92.451 0 -39.409 0 -13.636 -1 0 1 0 0 0 40.009 -288.7 75.36
(Others nearly zero) v3 (u1) 0 -68.544 113.96 0 1.5708 0 -15.849 -1 0 0 1 0 0 86.725 -723.2 65.98
v4 0 -3.3375 -57.009 0 -58.47 0 -8.6941 -1 0 0 0 1 0 -5.5638 117.38 66.75 -20.0007
v5 0 8.29469 -31.309 0 -28.045 0 -8.3573 -1 0 0 0 0 1 -5.7682 92.988 40.5 4.882266
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0.099 0.290088
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0.901 1.368574
Tableau 4* Row zero 1 -2E-12 -1E-12 0 0 0 0 0 0 0 0 0 0 1000 1000 -2E-12
u2 in; v4 out v1 0 -206.49 -130.94 0 -27.184 0 0 -0.31 1 0 -0.69 0 0 -23.643 218.23 3.079
Remove complementary Slackness v2 0 -57.642 -190.5 0 -40.761 0 0 -0.14 0 1 -0.86 0 0 -34.605 333.5 18.59
(Others nearly zero) u1 0 4.32485 -7.1904 0 -0.0991 0 1 0.063 0 0 -0.06 0 0 -5.472 45.632 -4.163
v4 0 34.263 -119.52 0 -59.331 0 0 -0.45 0 0 -0.55 1 0 -53.137 514.11 30.56
v5 (u2) 0 44.4387 -91.401 0 -28.874 0 0 -0.47 0 0 -0.53 0 1 -51.499 474.35   5.706
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0.099
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0.901
Z x1 x2 x3 x4 x5 u1 u2 v1 v2 v3 v4 v5 h1 h2 RHS
Tableau 5* Row zero 1 -2E-12 -1E-12 0 0 0 0 0 0 0 0 0 0 1000 1000 -2E-12
v1 0 -235.74 -70.771 0 -8.1782 0 0 0 1 0 -0.34 0 -0.66 10.257 -94.01 -0.677
v2 0 -70.771 -163.49 0 -32.231 0 0 0 0 1 -0.7 0 -0.3 -19.391 193.36 16.91
u1 0 10.2566 -19.391 0 -3.9532 0 1 0 0 0 -0.13 0 0.133 -12.346 108.95 -3.401
v4 0 -8.1782 -32.231 0 -31.756 0 0 0 0 0 -0.04 1 -0.96 -3.9532 61.084 25.11
u2 0 -94.012 193.363 0 61.084 0 0 1 0 0 1.116 0 -2.12 108.95 -1004 -12.07
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0.099
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0.901
Z x1 x2 x3 x4 x5 u1 u2 v1 v2 v3 v4 v5 h1 h2 s RHS
Tableau 6 Row zero 1 -2E-12 -1E-12 0 0 0 0 0 0 0 0 0 0 1000 1000   -2E-12
Introduce s v1 (s) 0 -235.74 -70.771 0 -8.1782 0 0 0 1 0 -0.34 0 -0.66 10.257 -94.01 -0.68 -0.677
s in; v1 out v2 0 -70.771 -163.49 0 -32.231 0 0 0 0 1 -0.7 0 -0.3 -19.391 193.36   16.91
IGNORE u's u1 0 10.2566 -19.391 0 -3.9532 0 1 0 0 0 -0.13 0 0.133 -12.346 108.95   -3.401
Iterations here (!) v4 0 -8.1782 -32.231 0 -31.756 0 0 0 0 0 -0.04 1 -0.96 -3.9532 61.084   25.11
u2 0 -94.012 193.363 0 61.084 0 0 1 0 0 1.116 0 -2.12 108.95 -1004   -12.07
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116   0.099
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156   0.901
Tableau 7 Row zero 1 -2E-12 -1E-12 0 0 0 0 0 0 0 0 0 0 1000 1000 2000 -2E-12
Add Big M to s s 0 348.183 104.528 0 12.079 0 0 0 -1.48 0 0.505 0 0.972 -15.149 138.85 1 1
v2 0 -70.771 -163.49 0 -32.231 0 0 0 0 1 -0.7 0 -0.3 -19.391 193.36 0 16.91
u1 0 10.2566 -19.391 0 -3.9532 0 1 0 0 0 -0.13 0 0.133 -12.346 108.95 0 -3.401
v4 0 -8.1782 -32.231 0 -31.756 0 0 0 0 0 -0.04 1 -0.96 -3.9532 61.084 0 25.11
u2 0 -94.012 193.363 0 61.084 0 0 1 0 0 1.116 0 -2.12 108.95 -1004 0 -12.07
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0 0.099
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0 0.901
Tableau 8 New Row Zero 1 -696367 -209055 0 -24158 0 0 0 2954 0 -1010 0 -1944 31298 -3E+05 0 -2000 Ratio
x1 in; s out s (x1) 0 348.183 104.528 0 12.079 0 0 0 -1.48 0 0.505 0 0.972 -15.149 138.85 1 1 0.009567
v2 0 -70.771 -163.49 0 -32.231 0 0 0 0 1 -0.7 0 -0.3 -19.391 193.36 0 16.91 -0.10341
u1 0 10.2566 -19.391 0 -3.9532 0 1 0 0 0 -0.13 0 0.133 -12.346 108.95 0 -3.401
v4 0 -8.1782 -32.231 0 -31.756 0 0 0 0 0 -0.04 1 -0.96 -3.9532 61.084 0 25.11 -0.77905
u2 0 -94.012 193.363 0 61.084 0 0 1 0 0 1.116 0 -2.12 108.95 -1004 0 -12.07 -0.06243
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0 0.099 0.140707
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0 0.901 3.049334
Z x1 x2 x3 x4 x5 u1 u2 v1 v2 v3 v4 v5 h1 h2 s RHS
Tableau 9 Row Zero 1 -487311 -146295 0 -16906 0 0 0 2067 0 -706 0 -1361 22202 -2E+05 600.4 -1400
DONE! x1 0 1 0.30021 0 0.0347 0 0 0 -0 0 0.001 0 0.003 -0.0435 0.3988 0.003 0.003
v2 0 0 -142.25 0 -29.776 0 0 0 -0.3 1 -0.6 0 -0.1 -22.47 221.59 0.203 17.11
u1 0 0 -22.47 0 -4.309 0 1 0 0.04 0 -0.15 0 0.105 -11.9 104.86 -0.03 -3.431
v4 0 0 -29.776 0 -31.472 0 0 0 -0.03 0 -0.03 1 -0.93 -4.309 64.345 0.023 25.13
u2 0 0 221.586 0 64.345 0 0 1 -0.4 0 1.252 0 -1.85 104.86 -966 0.27 -11.8
x3 0 0 0.60197 1 0.0331 0 0 0 0 0 -0 0 -0 0.1484 -1.252 -0 0.098
x5 0 0 0.09782 0 0.9322 1 0 0 0 0 -0 0 -0 -0.1048 1.853 -0 0.899
DONE! 0.5521
x1 0.002872 0.4478
x3 0.098156 0.9999
x5 0.898972