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

f_max = f(X₀) = 13,5056179775281

	X0	grad f	sum CkAk
x1	2,52808988764045	1,79775280898876	1,79775280898876
x2	1,97752808988764	2,24719101123596	2,24719101123596

C_k - Lagrange multipliers at the Kuhn-Tucker,
A_k - 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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