5 Assets
Returns:  10.9176 13.6357 15.84892 8.694 8.3573
Var - Cov Matrix
367.843 264.69 292.1499 59.98 21.718
264.69 349.275 345.3725 98.53 45.6425
292.15 345.373 651.2748 29.2 1.56749
59.9763 98.5251 29.20177 127.5 70.8837
21.718 45.6425 1.567486 70.88 44.7809
A=H= mu1 mu2 mu3 mu4 mu5
1 1 1 1 1
Target Return: 10 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 = 10
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 -11000
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 -11000 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   10 0.630958
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 -369 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 0 184.3 1.838106
ignore neg coeff v2 0 -26.78 -52.132 0 90.932 136.5 -13.636 -1 0 1 0 0 0 21.792 0 217.9 2.39647
v3 0 156.482 214.954 0 328.06 341.9 -15.849 -1 0 0 1 0 0 41.093 0 410.9 1.252596
v4 0 -39.861 -73.401 0 -111.46 -55.49 -8.6941 -1 0 0 0 1 0 1.8425 0 18.43
v5 0 -20.638 -44.294 0 -70.024 -43.95 -8.3573 -1 0 0 0 0 1 0.0989 0 0.989
x3 0 0.68885 0.86035 1 0.5486 0.527 0 0 0 0 0 0 0 0.0631 0 0.631 1.150211
h2 (x5) 0 0.31115 0.13965 0 0.4514 0.473 0 0 0 0 0 0 0 -0.0631 1   0.369 0.817474
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 0 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 81.02
Remove complementary Slackness v2 0 -116.61 -92.451 0 -39.409 0 -13.636 -1 0 1 0 0 0 40.009 -288.7 111.4
(Others nearly zero) v3 (u1) 0 -68.544 113.96 0 1.5708 0 -15.849 -1 0 0 1 0 0 86.725 -723.2 144
v4 0 -3.3375 -57.009 0 -58.47 0 -8.6941 -1 0 0 0 1 0 -5.5638 117.38 61.74 -18.5003
v5 0 8.29469 -31.309 0 -28.045 0 -8.3573 -1 0 0 0 0 1 -5.7682 92.988 35.31 4.256394
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0.219 0.641613
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0.781 1.186068
Tableau 4* Row zero 1 -2E-12 -1E-12 0 0 0 0 0 0 0 0 0 0 1000 1000 0
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 -18.2
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 -12.55
(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 -9.088
v4 0 34.263 -119.52 0 -59.331 0 0 -0.45 0 0 -0.55 1 0 -53.137 514.11 -17.26
v5 (u2) 0 44.4387 -91.401 0 -28.874 0 0 -0.47 0 0 -0.53 0 1 -51.499 474.35   -40.64
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0.219
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0.781
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 0
v1 0 -235.74 -70.771 0 -8.1782 0 0 0 1 0 -0.34 0 -0.66 10.257 -94.01 8.554
v2 0 -70.771 -163.49 0 -32.231 0 0 0 0 1 -0.7 0 -0.3 -19.391 193.36 -0.545
u1 0 10.2566 -19.391 0 -3.9532 0 1 0 0 0 -0.13 0 0.133 -12.346 108.95 -14.51
v4 0 -8.1782 -32.231 0 -31.756 0 0 0 0 0 -0.04 1 -0.96 -3.9532 61.084 21.55
u2 0 -94.012 193.363 0 61.084 0 0 1 0 0 1.116 0 -2.12 108.95 -1004 85.98
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0.219
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0.781
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   0
Introduce s s in; v2 out v1 0 -235.74 -70.771 0 -8.1782 0 0 0 1 0 -0.34 0 -0.66 10.257 -94.01   8.554
Iterations here (!) v2 (s) 0 -70.771 -163.49 0 -32.231 0 0 0 0 1 -0.7 0 -0.3 -19.391 193.36 -0.54 -0.545
u1 0 10.2566 -19.391 0 -3.9532 0 1 0 0 0 -0.13 0 0.133 -12.346 108.95   -14.51
v4 0 -8.1782 -32.231 0 -31.756 0 0 0 0 0 -0.04 1 -0.96 -3.9532 61.084   21.55
u2 0 -94.012 193.363 0 61.084 0 0 1 0 0 1.116 0 -2.12 108.95 -1004   85.98
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116   0.219
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156   0.781
Tableau 7 Row zero 1 -2E-12 -1E-12 0 0 0 0 0 0 0 0 0 0 1000 1000 2000 0
Add Big M to s v1 0 -235.74 -70.771 0 -8.1782 0 0 0 1 0 -0.34 0 -0.66 10.257 -94.01 0 8.554
s 0 129.911 300.119 0 59.164 0 0 0 0 -1.84 1.293 0 0.542 35.595 -354.9 1 1
u1 0 10.2566 -19.391 0 -3.9532 0 1 0 0 0 -0.13 0 0.133 -12.346 108.95 0 -14.51
v4 0 -8.1782 -32.231 0 -31.756 0 0 0 0 0 -0.04 1 -0.96 -3.9532 61.084 0 21.55
u2 0 -94.012 193.363 0 61.084 0 0 1 0 0 1.116 0 -2.12 108.95 -1004 0 85.98
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0 0.219
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0 0.781
Tableau 8 New Row Zero 1 -259822 -600238 0 -118329 0 0 0 0 3671 -2587 0 -1085 -70190 710896 0 -2000 Ratio
x2 in; s out v1 0 -235.74 -70.771 0 -8.1782 0 0 0 1 0 -0.34 0 -0.66 10.257 -94.01 0 8.554 -0.12087
s (x2) 0 129.911 300.119 0 59.164 0 0 0 0 -1.84 1.293 0 0.542 35.595 -354.9 1 1 0.003332
u1 0 10.2566 -19.391 0 -3.9532 0 1 0 0 0 -0.13 0 0.133 -12.346 108.95 0 -14.51
v4 0 -8.1782 -32.231 0 -31.756 0 0 0 0 0 -0.04 1 -0.96 -3.9532 61.084 0 21.55 -0.66866
u2 0 -94.012 193.363 0 61.084 0 0 1 0 0 1.116 0 -2.12 108.95 -1004 0 85.98 0.44467
x3 0 0.34175 0.70457 1 0.045 0 0 0 0 0 0 0 0 0.1335 -1.116 0 0.219 0.311214
x5 0 0.65825 0.29543 0 0.955 1 0 0 0 0 0 0 0 -0.1335 2.1156 0 0.781 2.642691
Z x1 x2 x3 x4 x5 u1 u2 v1 v2 v3 v4 v5 h1 h2 s RHS
Tableau 9 Row Zero 1 0 0 0 0 0 0 0 0 0 0 0 0 1000 1000 2000 0
DONE! v1 0 -205.11 0 0 5.7734 0 0 0 1 -0.43 -0.04 0 -0.53 18.65 -177.7 0.236 8.79
x2 0 0.43286 1 0 0.1971 0 0 0 0 -0.01 0.004 0 0.002 0.1186 -1.183 0.003 0.003
u1 0 18.6502 0 0 -0.1306 0 1 0 0 -0.12 -0.05 0 0.169 -10.046 86.016 0.065 -14.45
v4 0 5.77338 0 0 -25.402 0 0 0 0 -0.2 0.094 1 -0.9 -0.1306 22.965 0.107 21.66
u2 0 -177.71 0 0 22.965 0 0 1 0 1.183 0.282 0 -2.46 86.016 -774.8 -0.64 85.34
x3 0 0.03677 0 1 -0.0939 0 0 0 0 0.004 -0 0 -0 0.0499 -0.282 -0 0.217
x5 0 0.53037 0 0 0.8968 1 0 0 0 0.002 -0 0 -0 -0.1685 2.465 -0 0.78
DONE!
x2 0.003
x3 0.217
x5 0.78