Task 10
Find maximum of the function
f = -0,412x12 - 2,217x22 - 2,463x32 - 1,947x42 - 12,359x52 - 1,338x1x2 + 0,202x1x3 + 1,334x1x5 + 1,046x2x5 + 0,876x3x4 + 1,104x3x5 + 0,98x4x5 + 66,5x1 + 94,9x2 + 215,5x3 + 290,35x4 + 284,95x5
subject to
100x1 + 200x2 + 300x3 + 400x4 + 500x5 < 1000
-x1 - x2 - x3 - x4 - x5 < 0

If the function is given in matrix form f(X) = (X,QX) + (L,X), then
Q =   -0,412   -0,669   0,101   0   0,667
  -0,669   -2,217   0   0   0,523
  0,101   0   -2,463   0,438   0,552
  0   0   0,438   -1,947   0,49
  0,667   0,523   0,552   0,49   -12,359

L =   66,5  
x1
  94,9
x2
  215,5
x3
  290,35
x4
  284,95
x5



Outcome

fmax = f(X0) = 1115,12015932254

    X0   grad f   sum CkAk
x1
  23,3825873581988   68,6254120342847   68,6254120342847
x2
  -16,9568951813581   137,250824068569   137,250824068569
x3
  3,37274623216637   205,876236102854   205,876236102854
x4
  4,4557115362571   274,501648137139   274,501648137139
x5
  -1,48197636740202   343,127060171423   343,127060171423
Ck - Lagrange multipliers at the Kuhn-Tucker,
Ak - vector coefficients of left side of constraints number "k",

Execution constraints and Lagrange multipliers
  AkX0     B     Ck
  1000
<
  1000
+
  0,686254120342847
  -12,7721735778621
<
  0     0
Yellow highlighted lines that match the active inequalities at X.

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