Task 2
Find maximum of the function
f = -4x12 + 2x22 - 45x52 + 2x1x4 + 6x3x4 + 50x4x5 + 23x3
subject to
4x1 - x4 < 45
-2x2 - x3 - 5x4 < 60
7x1 + 3x5 < 21
-x1 + x2 - x3 + x4 - x5 < 54
-x3 < 0
x2 < 650

If the function is given in matrix form f(X) = (X,QX) + (L,X), then
Q =   -4   0   0   1   0
  0   2   0   0   0
  0   0   0   3   0
  1   0   3   0   25
  0   0   0   25   -45

L =   0  
x1
  0
x2
  23
x3
  0
x4
  0
x5



Outcome

Function is unbounded, for example, on the ray M0 + Vt, t > 0:
  f = at2 + bt + c
  a = 0,549637286954456
  b = 357,308983512125
  c = -2640767,75418336
    M0   V
x1
  -57,2284847534327   0,019601766510807
x2
  309,719844138243   -0,511984123065805
x3
  384,434453829519   0,631932915915469
x4
  -212,169107051433   0,078407066043228
x5
  139,830691767468   -0,045737455191883

Execution constraints:
Ak - vector coefficients of left side of constraints number "k", Bk - right side of constraints number "k".
  (Ak , M0)     Bk   (Ak ,V)
  -16,7448319622976
<
  45   0
  56,9713931511631
<
  60   9,71445146547012E-17
  18,8926820283736
<
  21   -1,38777878078145E-17
  -369,485923756744
<
  54   -1,03937428425697
  -384,434453829519
<
  0   -0,631932915915469
  309,719844138243
<
  650   -0,511984123065805
Yellow highlighted lines, that match planes of constraints polyhedron, that are parallel to the ray. In the last column of this row's the number is not zero only due to computational error.
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