Task 8
Find minimum of the function
f = 0,2x12 + 0,2x22 - 2,4x1 - 5,2x2
subject to
2x1 + x2 < 15
13x1 + 20x2 < 260
x1 < 0
x1 < 0

If the function is given in matrix form f(X) = (X,QX) + (L,X), then
Q =   0,2   0
  0   0,2

L =   -2,4  
x1
  -5,2
x2



Outcome

fmin = f(X0) = -33,8

    X0   grad f   sum CkAk
x1
  0   -2,4   -2,4
x2
  13   0   1,11048618399018E-16
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
  13
<
  15     0
  260
<
  260
-
  5,55243091995089E-18
  0
<
  0
-
  -2,4
  0
<
  0     0
Yellow highlighted lines that match the active inequalities at X.

Remark. It seems, that the author of tasks had intended last two conditions given in the form:
x1 > 0
x2 > 0
In this case, the site (area D) must specify inequalities:
-x1 < 0
-x2 < 0


to table of results