Task 7
Find maximum of the function
f = -528x12 - 324x22 - 121x32 + 828x1x2 + 506x1x3 - 396x2x3 - 3082x1 + 2412x2 + 1474x3
subject to
-21x1 + 18x2 + 11x3 > 64
73x1 - 54x2 - 33x3 < -194
-46x1 + 36x2 + 22x3 > 135
-23x1 + 17x2 + 11x3 < 67

If the function is given in matrix form f(X) = (X,QX) + (L,X), then
Q =   -528   414   253
  414   -324   -198
  253   -198   -121

L =   -3082  
x1
  2412
x2
  1474
x3



Outcome

fmax = f(X0) = 4496

    X0   grad f   sum CkAk
x1
  4   146   146
x2
  3   -108   -108
x3
  9,81818181818182   -66   -66
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
  78
>
  64     0
  -194
<
  -194
+
  2
  140
>
  135     0
  67
<
  67
+
  -8,73850657817141E-16
Yellow highlighted lines that match the active inequalities at X.


Local maxima


...... 1 ......

fmax = f(X0) = 4492

    X0   grad f   sum CkAk
x1
  -2   42   42
x2
  1   -36   -36
x3
  0,363636363636364   -22   -22
Execution constraints and Lagrange multipliers
  AkX0     B     Ck
  64
>
  64
-
  -2
  -212
<
  -194     0
  136
>
  135     0
  67
<
  67
+
  1,29010181676259E-16

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