Task 8
Find minimum of the function
f =
0,2x_{1}^{2}
+ 0,2x_{2}^{2}
 2,4x_{1}
 5,2x_{2}
subject to
2x_{1} + x_{2} < 15
13x_{1} + 20x_{2} < 260
x_{1} < 0
x_{1} < 0
If the function is given in matrix form f(X) = (X,QX) + (L,X), then
L = 
2,4 

x_{1} 
5,2 
x_{2} 
Outcome
f_{min} = f(X_{0}) = 33,8

X_{0} 
grad f 
sum C_{k}A_{k} 
x_{1} 
0 
2,4 
2,4 
x_{2} 
13 
0 
1,11048618399018E16 
C_{k}  Lagrange multipliers at the KuhnTucker,
A_{k}  vector coefficients of left side of constraints number "k",
Execution constraints and Lagrange multipliers
A_{k}X_{0} 

B 

C_{k} 
13 
< 
15 

0 
260 
< 
260 
 
5,55243091995089E18 
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:
x_{1} > 0
x_{2} > 0
In this case, the site (area D) must specify inequalities:
x_{1} < 0
x_{2} < 0
to table of results