100
− p = p − 10 110 = 2 p 55 = p
D(55) = 100
− 55 = 45
45 90/2/2 = 1012, 5
∗
pD
− t = p
100
− p
− 10 100 − p = p − 10 − 10 120 = 2 ∗ p D
D
= p S D
D
60 = p D 60
− 10 = 50 = p
Q = 100
S
− 60 = 40
S
T = 40 10 = 400
∗
T T = F T = 40 40/2 = 800
∗
HT V = 2025
− 800 − 800 − 400 = 25
pD = p S 1, 1
∗
− 0, 5 ∗ p 195 − 0, 55 ∗ p 195
= 2 pS
∗ − 60 = 2 ∗ p − 60 255 = 2, 55 ∗ p D
S
S
S
100 = p S 1, 1 100 = 110 = p D
∗
Q = 200
195
− 60 = 140
− 0, 5 ∗ p = 2 ∗ p − 60 255 = 2, 5 p
p = 102 Q = 2 102
∗
HT V = (144
190
− 60 = 144
− 140) ∗ 10/2 = 20
− p = p − 20 210 = 2 p 105 = p
Q = 105
HT V = (130
− 20 = 85
− 80) ∗ (85 − 60)/2 = 625
U =
0, 2 =− = −1 −MU MU 0, 2
MRS =
x y
x+y 5
MRS =
−∞
U = (3 + 2) 8 = 40
·
40 = (x + 2)y 40 = y x+2
MRS =
− MU MU
x y
MRS =
− x +y 2 = − 85
40 = (x + 2)y ∆y | ∆x | = 12 = 2
10 =
xy 3
100 = xy 3
3
100 = y x
MU x =
MRS =
−
· √ · ·
y 3 0, 5 x−0,5
·
3 x y 1/2 M U y = 2 MU x y3 0, 5 x−0,5 √ = = 3 x·y 1/2 MU y
−
·
2
− 3xy
200 =
xy3
y 4 = 3x 3 y = 4x
40000 = 64x4 x = 5 y = 4x = 20
U = x+52y
100000 = 10000x1 + 50000x2
maxx1 = 10 maxx2 = 2 150000 100000
≥ 25000x + 50000x
100000
≥ 10000x + 20000x
1
≥ 10000x + 50000x 1
2
2
1
2
m = 300000 ∆m =
200000 100 12
100000
≥ 12000x + 50000x
100000 40000 = 12500(x1 50000 = 8000(x1
− 5) + 50000x
2
− 5) + 20000x
2
1
2
≥ 12500x + 50000x 1
100 12,5
=8
2
≥ x
1
≥ x
1
100000 = 12000x1 + 50000x2
5
100000 = 10000x1 + 50000x2
5
5 < x1 5 < x1 100000 = 10000x1 + 50000x2
6, 5
≥ x
1
200000 = 10000x1 + 50000x2
2
≥ x
2
100000 + 10000x2 = 10000x1
x = 15
− 1, 25y
y = 4 x = 15
− 1, 25y
x = 10 400 = 10 px 40 = p x m = 15 px = 600 200 py = = 50 4 900 = 30x + 100y
36000 = 2400x + 600y
36000 = 3000x + 600y 45000 = 3000x + 600y
60
≥ y
45000 = 3000x + 600y
36000 = 2400x + 600y
7
≥ x
66000 x 1200 66000
∗
− 33600 = 32400
≥ x ∗1200−max[0;(x−10)∗(1200∗0, 1)]
− max[0;(x − 10) ∗ (1200 ∗ 0, 1)] = 33600
x = 66000/1200 + 66000/12000 = 55 + 5, 5 = 60
12000 = 2400x + 800y
x =
m/2 1500 = = 15 px 100
y=
m/2 1500 = = 10 py 150
px = 125 x = 1500/125 = 12 y = 10
x = 2250/125 = 18 y = 2250/150 = 15
y = 3x U = 3y + x
|MRS |=
y = 9
1 3
− 0, 3x
U = min[x; 2y] M RS =
−∞
MRS = 0
5340 = 160x + 125y x = 2y 5340 = 445y 12 = y 24 = x
5340 = 10 125 + 20 px
∗
∗
px = 204, 5
|MRS | = pp
x y
1 20 = x 100 x = 5 300 y=
− 5 ∗ 20 = 2 100
x1 =
4500 p1
2y y 30 = = = 0, 75 |MRS | = 0,0, 2x x 40 y(x) = 0, 75x
m/2 px m x(m) = 60 m/2 y(m) = py m y(m) = 80 x(m) =
y (x) = 0 m 1800 y(m) = 0
x(m) =
x( px ; m) =
m px
px < 1875 x( px; m) = 0
px > 1875
x( px ; m) [0;
∈
m ] px
Qk = 2 Qt
∗
Qt ( pt ) =
7700 160+ pt
U N = x 0,5 y0,5 U T = x 0,2 y 0,8
·
·
x = 1000 = 10 100 y = 1000 = 50 20
x =
300 100
=3
y = 1200 = 60 20
mN /2 1000 = px px mN /2 1000 = = py py mT /5 300 = = px px 4mT 1200 = = 5 py py
DxN = DyN DxT DyT
mN /2 + mT /5 1300 = px px mN /2 + mT 4/5 2200 Dy = = py py
Dx =
∗
x = 15 py = 20 m = 900 T H x = 0 T H y =
−15 HH = 22, 5 − 15 = 7, 5 HH = 22, 5 − 30 = −7, 5 JH = −7, 5 JH = −7, 5 x
y
x y
y = 30 U = 450
U = 450
x = y =
√
450
≈ 21, 21
T H x = 0 T H y =
−15 HH = 21, 21 − 15 = 6, 21 HH = 21, 21 − 30 = −8, 79 JH = −6, 21 JH = −6, 21 x
y
x y
∆m = 300
∆m = 42, 42 20
∗ − 600 = 248, 53
HH = T H = JH = 0
T H =
JH =
−1, 25
−1, 25
HH = 0
T H = HH =
−11, 25
JH = 0
−11, 25
T H = 9 HH = 11, 25 HH = 11, 25 60/50 = 13, 5
∗
JH = JH =
−2, 25
1 x
x = 9
y = 0
T H = 9
−2, 25
= 10/100
x = 10
1 = 20/100 x x = 5 x = 4, 5 T H x =
−4, 5
T H y = 0 HH x = 5
− 9 = −4 HH = ln(9) − ln(5) = 0, 588 JH = −0, 5 JH = −0, 588 y
x
y
T H x =
−4, 5
T H y = 0 HH x = 5
− 9 = −4 HH = (9 ∗ 20 − 5 ∗ 20)/100 = 0, 8 JH = −0, 5 JH = −0, 8 y
x y
1 = 10/40 x x = 4 y = 1, 25
T H x =
−5
T H y = 1.25 HH x = 4
− 9 = −5 HH = (90 − 40 + ((ln(9) − ln(4) − 1, 25) ∗ 40))/40 = 0, 811 y
JH x = 0 JH y = 0, 439
T H x =
−5
T H y = 1.25 HH x = 4
− 9 = −5
HH y = 1, 25 JH x = 0 JH y = 0
D = 400 − 3 p ≥ p 150 ≥ p > 100 D = 300 − 2 p 100
p > 150
D = 0
150 p > 150
0
p > 40
20
− 0, 5 p 35 − 1, 5 p 45 − 3, 5 p
≥ p > 15 15 ≥ p > 5 5 ≥ p 40
p > 100 100
≥ p > 20
0 100 (20
·
− 0, 2 p) = 2000 − 20 p
≥ p > 100
20
≥ p ≥ 0
δD( p) p δp D( p)
=
·
δD( p) δp
·
p D( p)
δD 1 ( p1 ,p2 ,m) δp1 δD1 ( p1 ,p2 ,m) δp 2 δD1 ( p1 ,p2 ,m) δm
· ·
δD1 ( p1 ,p2 ,m) δm
· ·
δD1 ( p1 ,p2 ,m) δm
· ·
−4 ·
−
p = − p150 2 150/p =
·
·
p1 D1 ( p1 ,p2 ,m)
m D1 ( p1 ,p2 ,m)
mp2 p31
=
m D1 ( p1 ,p2 ,m)
m p21
5
p2 p21
p2 mp2 p2 1
5
mp2 p2 1
p1 mp2 p2 1
m
mp22 p41
mp2 p31
p22 p31
6 p1
p1
16
p2
16
mp2 2 p3 1
mp2 2 p3 1
m
16
mp2 2 p3 1
3m 4 p2 p21
8 p1
5
2
p2 3m−4p2 p1 m
3m−4p 2 p 2 1
p1 3m−4p2 2 p 1
4 p2 3m 4 p2
3m 3m 4 p2
x( p) = 100
δD( p) δp
·
p D( p)
=
−1 ·
− = −2/3
−2 ∗ 5 · = −2 =5 · =1 =5 · =1 = −3 · 16 = −3 · = 2 · 16 =2 · = 16 · =1 = −2 − · = −1 =− · = − − = · = −
p1 D1 ( p1 ,p2 ,m)
p2 D1 ( p1 ,p2 ,m)
p 200 4 p
−1
p1 D1 ( p1 ,p2 ,m)
p2 D1 ( p1 ,p2 ,m)
·
− 20 p + 50 · (80 − 4 p) = 6000 − 220 p
p 200 4 p
m D1 ( p1 ,p2 ,m)
δD1 ( p1 ,p2 ,m) δp 1 δD1 ( p1 ,p2 ,m) δp 2
−4 ·
2000
p2 D1 ( p1 ,p2 ,m)
δD1 ( p1 ,p2 ,m) δp 1 δD1 ( p1 ,p2 ,m) δp 2
p 100 p
− = −1, 5
− p.
Dx = (100 py
− 5 p ) ∗ p /2m x
px = 5 py = 100
δDx ( px ,py ,m) δp x δDx ( px ,py ,m) δp y δDx ( px ,py ,m) δm
· · ·
px Dx ( px ,py ,m)
5 py = −2m
py Dx ( px ,py ,m)
=
m Dx ( px ,py ,m)
=
px 5 px (100−5px )py 100 5 px 2m py 100 5 px (100−5px )py 2m 2m (100 5 px ) py m (100−5px )py 2m2 2m
−
−
= −−
·
−
=1
·
·
=
−1
y
m = 50
px
Q = 20L
M P L = 2K = 20
√ Q = 20 L Q = 20L L MP L = 10L
AP L =
√
√
√ √ 1, 1Q = 1, 1 · 20 L √ Q = 20 L
1, 1Q = 20 1, 21L
M P L = (10L) = 10
1/4 1/4
T R = pq = 4000x1 x2 T C = 16x1 + 25x2
1/4 1/4 (16x1 + 25x2 ) π = 4000x1 x2 δπ −3/4 1/4 16 = 0 = 1000x1 x2 δx 1 δπ −3/4 1/4 25 = 0 = 1000x2 x1 δx 2 164 x2 = 3/4 4 (1000x− ) 1
− − −
0 = 1000
4
16
−3/4 )4 (1000x 1
−3/4
1/4
x1
− 25
4
1000 = x 21 3 16 25 3125 = x 1
·
164 x31 = 2000 = x 2 10004 y = (2000 3125)1/4 = 50
·
π = 50 4000
·
− 16 · 3125 − 25 · 2000 = 100000
y = K 1/3 L1/3 p = 1 w = 1 r = 2
p3 27wrk2 3 L = rk wp2 27 1 K = 108 1 L = 54 1 1 π = 18 54 p3 Q = 3 27wr 2 k
K =
·
1 1 = 54 108 p3 p2 = 2 rk w 27 9wrk
− − 2 ·
·
y = 2K 0,25 L0,5 K = 16
∗
π = 20 2K 0,25 L0,5 δπ δK
·
L0,5
= 10 K 0,75
10 = r k δπ δL
0,25
= 20 K L0,5
5 = w
− r
k
− wL − r K
=0
− w = 0
k
L = 64
∗
F C = 30 2
V C = 20Q
3
− 5Q + Q AC = 30/Q + 20 − 5Q + Q AV C = 20 − 5Q + Q MC = 20 − 10Q + 3Q
2
2
2
Q
≥ Q
A
QB
QA
F C = 256 2
V C = 138q
3
− 28q + 2q AC = 256/q + 138 − 28q + 2q AV C = 138 − 28q + 2q
2
2
AF C = 256/q
2
MC = 138
− 56q + 6q AC = −256/q − 28 + 4q = 0 2
q = 8
MC 8 = 138
− 56 · 8 + 6 · 64 = 74 AV C = −28 + 4q = 0
q = 7
MC 7 = 138
− 56 · 7 + 6 · 49 = 40
V C = 3y 3 F C = 294 AV C = 3y2 AF C =
294 y 2
− 36y
2
+ 180y
− 36y + 180 294 y
AC = 3y
− 36y + 180 + MC = 9y − 72y + 180 AC = 6y − 36 − =0 6y − 36y − 294 = 0 2
294 y2
3
2
y=7
AV C = 6y y=6
− 36 = 0
AC 7 = 117 AV C 6 = 72 AC = M C AV C = M C lim MC = 180
y
→0
lim AV C = 180
y
→0
q2 + 400T T q2 T C = 1000 + 400000 q AC = 1000 + 400000 q q MC = 500
T C =
q + 400000 1000 q
AC = M C
=
q = 20000
AC = 0
q = 20T
T = 2000
q = 40000
T = 3000
q = 60000
q2 + 1000
400000 <
q2 + 2000
800000
q2 + 3000
1200000
q > 28284, 27 q2 + 2000
800000 <
q > 48989, 79
MRTS =
√ K √ K 3
1
L 4 2L 4
=
K = 5L 1
MP L MP K 5 2
√
=
w rk
1
√
Q = 4L 4 K = 4L 4 5L
Q
√
4 5
4 3
= L
q 500
L =
K 5 1
√
1
√
Q = 4L 4 K = 4( K ) 4 K 5
√ 4 5
q
4 3
= K
4
4
T C = wL + Krk = 0, 8079q 3 1
1
MC = 34 0, 8079q 3 = 1, 077q 3 δQ K δK Q
1
2L 4 K K 4L 14 K
= √
√ =
1 2
T C = wL = wQ = 2Q T C = r K K = r K Q4 = 2, 5Q AC = AV C = M C = 2, 5
MRTS =
K = L
p < 2, 5
50100
2K = L K = L = K =
L 2
√ 4Q 4
Q 4
4
T C = wL + rK K
√ T C = 50 4Q + 100 4
K = Q =
4
Q = 4
√
100 4 4Q
pL L 100 L4 p2L 10000 10 4 Q pL
√
L = √
L = 5K T C = 76500 = wL + rK K = 20L + 200K = 300K = 60L K = 255 L = 1275 Q = 1275
K = 255 L = 1275
T C = q (w + 0, 2rk ) = q (20 + 40) = 60q
C (y) = y 3
V C = y 3
− 12y
2
F C = 98 AC = y 2 AV C = y 2 AF C =
98 y 2
+ 60y
− 12y + 60 +
− 12y + 60
MC = 3y
− 24y + 60 AC = 2y − 12 − = 0 98 y2
y=7
AC (7) = 39 AV C = 2y y=6
− 12
AV C (6) = 24 M C (6) = AV C (6) = 24 MC (7) = AC (7) = 39 AV C (0) = M C (0) = 60
98 y
− 12y
2
+ 60y + 98
p = M C 48, 75 = 3y2 3y 2
− 24y + 60
− 24y + 11, 25 = 0
y1 = 0, 5 y2 = 7, 5
C (y) = q 2 + 20q + 400
V C = q 2 + 20q F C = 400 AV C = q + 20 AF C =
400 q
AC = q + 20 +
400 q
MC = 2q + 20
p = M C = 50 = 2q + 20 q = 15 π = 50 15
2
· − 15 − 20 · 15 − 400 = −175
cv (y) = y2 /F
AC = AC =
1 200
y = 8000
−
200 1600 y2
AC (8000) = 80 MC =
2y 200
·
=0
y + 200 y1600 200
·
