Task 13
Find maximum of the function
f = -2x12 - 3x22 + 4x1x2 + 4x1 + 4x2
subject to
4x1 + 5x2 < 20
x1 < 4
-x1 < 0
-x2 < 0

If the function is given in matrix form f(X) = (X,QX) + (L,X), then
Q =   -2   2
  2   -3

L =   4  
x1
  4
x2



Outcome

fmax = f(X0) = 13,5056179775281

    X0   grad f   sum CkAk
x1
  2,52808988764045   1,79775280898876   1,79775280898876
x2
  1,97752808988764   2,24719101123596   2,24719101123596
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
  20
<
  20
+
  0,449438202247191
  2,52808988764045
<
  4     0
  -2,52808988764045
<
  0     0
  -1,97752808988764
<
  0     0
Yellow highlighted lines that match the active inequalities at X.

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