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
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.
to table of results