3. X 1$, Y 1,5$, I 12$. Y = 24/X.
1) , : , , .
2) ; .
3) .
. : M = PX X + PY Y. , :
PY Y = M - PX X, Y = M /PY - PX /PY*X, :
M/PY , Y X=0, Y;
- PX /PY X, , Y , X, - PX /PY = -DY/DX.
1. . , : 12 = 1X + 1,5Y.
Y = 8 2/3X.
Y = 24/X.
) , , . :
1. Y = 8 2/3X
2. Y = 24/X
Y :
8 2/3X = 24/X → 36 = 12 X X2. X = 6, Y = 24/X = 24/6 = 4.
, 6 . . X 4 . . Y.
) . :
MRSxy = Px/Py = 1/1,5 = - 2/3.
MRSxy :
Y΄= (24/X)΄ = - 24/ X2
, :
24/ X2 = 2/3 → X2 = 24:2/3 = 36 → X = 6.
X = 6 : Y = 24/X = 24/6 = 4.
, 6 . . X 4 . . Y.
2. .
. : 12 = 1*X + 1,5*Y. . Y, . X, . Y, . , (N), , , :
N = = = = = const.
. .
Y (.) | DY | X (.) | DX | N xy | |
K | |||||
L | -2 | +3 | -2/3 | ||
M | -2 | +3 | -2/3 | ||
N | -2 | +3 | -2/3 | ||
F | -2 | +3 | -2/3 |
3. Y = 24/X , X Y. , X Y.
|
|
Y (.) | DY | X (.) | DX | MRS=-DY/+DX | |
k | |||||
l | -6 | +2 | |||
m | -2 | +2 | |||
n | -1 | +2 | 0.5 |
MRS=-DY/+DX, , . N, , MRS = -DY/+DX = MUx/MUy ↓.
, (6X + 4Y), .
3. . M . .
Y
4 --------------- M
X
3 6 9 12 15 18 21
, . .
. .