Taller 9 Y 10
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TALLER No. 9
1 C ( x) = 10 + 2 x C ( x) = 2
2 C(x) = 40 + (In2)x 2
( 2)
C(x) = 0 + (In2)(2x) + x 2 1 x2 2 12 C(x) = 2(1) In2 + 2 1 C(x) = 2In2 + 2 C(x) = 2In2 + 0,5 C(x) = 2xIn2 +
C(x) = 1,38 + 0.5 C(x) = 1,88
3 C ( x ) = 0.0001x 3 − 0.09 x 2 + 20 x + 1200 C ( x ) = 0.0001x 3 − 0.09 x 2 + 20 x + 1200 C ( x ) = 0.0003 x 2 − 0.18 x + 20 C ( x ) = 0.0003(1) − 0.18(1) + 20 C ( x ) = 0.0003(1) − 0.18 + 20 C ( x ) = 0.0003 − 0.18 + 20 C ( x ) = 19.82 2
4 C ( x ) = 10 −6 x 3 − (3 *10 −3 ) x 2 + 36 x + 2000
C ( x ) = 10 −6 (3 x 2 ) − (3 * 10 −3 ) x 2 + 36 x + 2000 C ( x ) = 30 x −4 − 30 −3 ( 2 x ) + x 2 ( 0 ) + 36 C ( x ) = 30 x −4 − 60 x −2 + 36 C ( x ) = 30(1)
−4
− 60(1)
−2
+ 36
C ( x ) = 30 −4 − 60 −2 + 36 C ( x ) = 0.0000012 − 0.00027 + 36 C ( x ) = −0.0002765 + 36 C ( x ) = 35.49
5 R ( x ) = x − 0.01x 2 R ( x ) = 1 − 0.02 x
R ( x ) = 1 − 0.02(1) R ( x ) = 0.98
6 R ( x) = 5 x − 0.01x 5 2 0.05 3 2 x 2 0.05 3 2 R( x) = 5 − (1) 2 R( x) = 5 −
R( x) = 5 −
0.05 2
3
R ( x ) = 5 − 0.025
2
3
2
= 5 − 0.0039
R ( x ) = 4.9961
7
R ( x ) = 0.1x − 10 −3 x 2 − 10 −3 x
[
5
2
]
7 5 R ( x ) = 0.1 − 10 −3 ( 2 x ) + x 2 ( 0 ) − 10 −3 5 x 2 + x 2 ( 0 ) 2 7 R ( x ) = 0.1 − 20 x −2 + 0 − 25 x 2 + 0
[
]
R ( x ) = 0.1 − 20 x −2 − 25 x R ( x ) = 0.1 − 20(1)
7
2
− 25(1)
−2
7
2
7
R ( x ) = 0.1 − 20 −2 − 25 2 R ( x ) = 0.1 − 0.0025 − 0.0000128 R ( x ) = 0.097
(
8 R ( x ) = 100 x − ( Log5) x 3 1 + x
)
R ( x ) = 100 x − 0,69 x 3 1 + x 2 1 1 2 R ( x ) = 100 − 0,69 x 3 0 + 1 2 x 2 + 1 + x 2 2,07 x 1
(
)
R ( x ) = 100 − 0,345 x
5
R ( x ) = 100 − 0,345(1) 5
2 5
(
+ 2,07 x 2 + 2,07 x 2
Q P
D
X = 100 − 4 p I = p.Q
I = p (100 − 4 P ) I = 100 p − 4 p 2 I = 100 − 8 p I = 100 − 8(1) I = 100 − 8 I = 92
2
+ 2,07(1) + 2,07(1) 2
R ( x ) = 100 − 0,345 2 + 2,07 2 + 2,07 R ( x ) = 100 − 0,69 + 4,28 + 6,16 R ( x ) = 110,651
9 x + 4 p = 100
5
5
2
5
2
)
10 Q
x + p = 10 P D x = 10 − p
x
1
2
= 10 − p
x = (10 − p ) I = p.Q
2
[ ] I = p[2(10 − p ) + (10 − p ) (1) ] I = p (10 − p )
2
2
I = p ( 20 p − 2 p ) + (10 − p ) I = 20(1) − 2(1) + (10 − 1) 2
2
2
I = 20 − 2 2 + 9 2 I = 20 − 4 + 81 I = 97
11
x
3
2
+ 50 p = 1000
I = 16 x
3
I = 16 x
3
I = 16 x
3
I = 16(1) 3
2
= 1000(16 ) − 50(16) p
2
= 16000 − 800 p
2
− 16000 − 800 p
3
2
− 16000 − 800 p
I = 16 − 16000 − 800 p I = 64 − 16000 − 800 p I = 15936 + 800 p 2
12 10 p + x + 0.01x 2 = 700 x + 0.01x 2 = 700 − 10 p I = x + 0.01x 2 = 700 − 10 p I = 10 x + 0.1x 2 − 7000 + 100 p I = 10(1) + 0.1(1) − 7000 + 100 p I = 10 + 0.1 − 7000 + 100 p I = 10.1 − 7000 + 100 p 2
I = −6989.9 + 100 p
13 U = I − P
U = 100 P − 4 P 2 − (100 + 5 x ) U = 100 P − 4 P 2 − 100 − 5 x U = 100 − 8 P − 5 U = 95 − 8 P
14 U = I − C
( ) U = P (10 − P ) − 60 − X U = (10 P − P ) − 60 − X U = 2(10 P − P )(10 − 2 P ) − 1 U = P 10 − P 2 − ( 60 + x ) 2
2 2 2
U = 20 P − 2 P (10 − 2 P ) − 1 2
15 U = I − C U = 16 x
3
U = 16 x
3
U = 15 x
3
2
3 − 1600 + 800 P − 50 + x 2
2
− 1600 + 800 P − 50 − x
2
− 1950 + 800 P
3
2
(15 x ) 2 + 800 2 1 U = 45 x 2 + 800 2 1 U = 45 ( 25 ) 2 + 800 2 U = 823 .7 U =3
1
16 U = I − C
U = 10 x + 0.1x 2 − 7000 + 100 p − (1000 + 0.1x 2 ) U = 10 x + 0.1x 2 − 7000 + 100 p − 1000 − 0.1x 2 U = 10 x − 8000 + 100 p
A U U U U
B = 10 x − 8000 + 100 p = 10 (100 ) − 8000 + 100 p = 1000 − 8000 + 100 p = 7000 + 100 p
U U U U
= 10 x − 8000 + 100 p = 10 x − 8000 + 100 (10 ) = 10 x − 8000 + 1000 = 10 x − 7000
17 F (u ) = 95 − 8 p
F (u ) = 95 − 8( 0 ) F (u ) = 95
0 = 95 − 8 p p = 95 − 8 p = 87
18 F (u ) = 20 p − 2 p 2 (10 − 2 p ) − 1
F (u ) = 20( 0 ) − 2( 0 ) (10 − 2( 0 ) ) − 1 F (u ) = 0 − 2( 0) (10 − ( 0 ) ) − 1 2
F (u ) = 10 − 1 F (u ) = 9
0 = 20 p − 2 p 2 (10 − 2 p ) −1 0 = 20 p − 20 p 2 + 4 p 3 −1 0 = 20 p − 20 p 2 + 3 4 p 3 −1 0 = 20 p − 20 p + 4 p −1 0 = 4 p −1 p = 4 −1 = 3
19 p1 = 4 Q1 = 100 p 2 = 5 Q 2 = 80 p 2 − p1 Q 2 − Q1 5−4 m= 80 − 100 1 m= − 20 m = 0.005 m=
p − p1 = m( Q − Q1)
p − 4 = 0.05( Q − 100 ) p − 4 = 0.05Q + 5 p = 0.05Q + 5 + 4 p − 0.005Q − 4 = 5 p − 0.05Q = 9 0.05Q = 9 − p 9− p Q= 0.05
I = P.Q 9 − P I = P 0.05 9P − P 2 I = 0.05 0.05( 9 − 2 P ) − 9 P − P 2 ( 0 ) I = 0.05 2 0.05( 9 − 2 P ) − 0 I = 0.025 0.45 − 0.1 I = 0.025 0.45 − 0.1 I = 0.025 0.35 P= 0.0025 P = 140
20
P1 = 1 P 2 = 1.50 Q1 = 20000 Q 2 = 45000 1.50 −1 M = 15000 − 20000 0.50 M = = 0.0001 − 5000 P − P1 = M ( Q − Q1) P −1 = 0.0001( Q − 2000 ) P −1 = 0.0001Q + 2 P = 0.0001Q + 3 P + 0.0001Q = 3 3−P 0 = 1 P 0.0001
3P − P 2 0.0001 0.0001( 3 − 2 P ) − 3P − P 2 ( 0 ) 0= 0.00001 2 0.003 − 0.0002 P 0= 0.0000001 U = I − [CF + ( CV .Q ) ] 3P − 2 P U = − [10000 + ( 0.80Q ) ] 0.0001 3P − 2 P U = −10000 − 0.80Q 0.0001 0.0003 − 0.002 P U = − 0.80Q 0.0000001 0.0003 − 0.002 P 0= − 0.80Q 0.0000001 0.0003 − 0.0002 P= − 0.80Q 0.0000001 P = 10000 − 0.80 0=
P = 9999..2
A U U U U U
B 3P − P 2 = −10000 − 0.80Q 0.0001 3(1.80 ) − 1.80 2 = − 10000 − 0.80Q 0.0001 5.4 − 3.24 = −10000 − 0.80Q 0.0001 2.16 = − 10000 − 0.80Q 0.0001 = 11600 − 0.80Q
21 C ( x ) = AX
2
C ( x ) = 2 AX
U U U U U
C 3P − P 2 = − 10000 − 0.80 Q 0.0001 3(1.90 ) − 1.90 2 = − 10000 − 0.80 Q 0.0001 5.7 − 3.61 = − 10000 − 0.80 Q 0.0001 2.09 = − 10000 − 0.80 Q 0.0001 = 10900 − 0.80 Q
+ BX + C 2
+B
+ BX + C X AX 2 BX C C’ ( x ) = + + X X X C C’ ( x ) = AX + B + X AX C’ ( x ) =
AX
2
AX + B + C X 2 AX 2 + 2 AXB + 2 AXC + AXB + B 2 + BC C’ ( x ) = X 2 ZX + 2 ZXC + ZXB + B 2 + BC C’ ( x ) = X C’ ( x ) =
22 NO ES VERDAD PORQUE NO TODS LAS VARIABLES QU ESTAN ELEVADAS ESTAN MULTIPLICANDO A LA X
23
C ( F ) = 4 + 0.36 I + 0.48 I 1.44 2 4 C ( F = 0.36 ) + I 4 ∆S + ∆C = ∆I
3
4
∆S = ∆I − ∆C ∆S = 16 − 4 + 0.36 I + 0.48 I ∆S = 16 − 4 = 12 ∆S = 16 − 0.36 = 15.64 ∆S = 16 − 0.15 = 15.52 ∆S = 12 − 15.64 I − 15.52 I ∆S = 15.64 +
46.56 4
3
4
3
4
3P − P 2 − 10000 − 0.80 Q 0.0001 3( 2 ) − 2 2 = − 10000 − 0.80 Q 0.0001 6−4 = − 10000 − 0.80 Q 0.0001 2 = − 10000 − 0.80 Q 0.0001 = 10000 − 0.80 Q
U = U U U U
TALLER No. 10
1
p dx e = x dp p dx e = x p dp
p 2 0( 0 ) − ( k )(1) x P2 2 p 0−k e= 2 x p e=
x p2 − xp 2 e= xp 2 e = −1 e=
p2 x
2 A x x x x
= 500(10 − p ) = 500(10 − 2 ) = 500( 8) = 4000
2 e = [500(10 − p ) ] 4000 2 e = [500( − 1) − (10 − p )( 0) ] 4000 2 2 e = ( − 500 + 0) = ( − 500 ) 4000 4000 − 1000 e= 4000 e = −0.25
B x x x x
= 500 (10 − p ) = 500 (10 − 5) = 500 ( 5) = 2500
5 e = [ 500 (10 − p ) ] 2500 5 e = [ 500 ( − 1) − (10 − p )( 0 ) ] 2500 5 5 e = ( − 500 + 0 ) = ( − 500 ) 2500 2500 − 2500 e= 2500 e = −1
C
x = 500 (10 − p ) x = 500 (10 − 6 ) x = 500 ( 4 ) x = 2000
5 e = 2000 5 e = 2000
[ 500 (10 − p ) ]
[ 500 ( − 1) − (10 − p )( 0 ) ] 5 5 e = ( − 500 + 0 ) = ( − 500 ) 2000 2000 − 30000 e= 2000 e = −1.5
3 A x = 400 − 100 p
x = 400 − 100 (1) x = 400 − 100 x = 300 p dx e = x dp 1 e = ( 400 − 100 p ) 300 1 e = ( − 100 ) 300 − 100 e= 300 e = −0.33
B x x x x
= 400 − 100 p = 400 − 100( 2 ) = 400 − 200 = 200
2 e = ( − 100 ) 200 − 200 e= 200 e = −1
C x x x x
= 400 − 100 p = 400 − 100( 3) = 400 − 300 = 100
3 e = = −100 100 − 300 e= 100 e = −3
4 A x p + =1 1000 8 x 2 + =1 1000 8 x + 0.25 = 1 1000 x = 1 − 0.25 1000 x = 0.75(1000 ) x = 750 p 2 p ( 0 ) − 8(1) e = 1 − ( 0 ) − 1000 8 82 750 2 8 e = 0 + 1000 750 64 8 2 e = 1000 − 64 750 2 63992 e = 750 64 2 e = ( 999875) 750 1999.75 e= 750 e = 2.66
B x 4 + =1 1000 8 x + 0.5 = 1 1000 x = 1 − 0 .5 1000 x = 0.5(1000 ) x = 500 4 e = ( 999875) 500 3999.5 e= 500 e = 7.9
C x 4 + =1 1000 8 x + 0.5 = 1 1000 x = 1 − 0 .5 1000 x = 0.5(1000 ) x = 500 4 e = ( 999875) 500 3999.5 e= 500 e = 7.9
5 x = 250 − 30 p + p 2
x = 250 − 30(12 ) + 12 2 x = 250 − 360 + 144 x = 34
(
12 e = 250 − 30 p + p 2 34 12 e = ( 0 − 30 + 2 p ) 34
)
12 e = ( − 30 + 2 p ) 34 − 360 + 24 p e= 34 − 360 + 24(12 ) e= 34 − 360 + 288 e= 34 e = −2.11 Cambio Porcentual en la demanda e= Cambio Porcentual en el Pr ecio CPD = ( CPP )( e ) CPD = ( 8.5% )( − 2.11) CPD = −17,935%
6 A p p p p
= 30 − 0.5 x = 30 − 0.5( 200 ) = 300 − 100 = 200
p = 300 − 0.5 x p + 0.5 x = 300 0.5 x = 300 − p 300 − p x= 0.5 200 300 − p e = 200 0.5 200 0.5( 0 − 1) − 300 − p ( 0 ) e = 0.5 2 200
A I = ( 300 − 0.5 x ) x
200 0.5( − 1) e = 200 0.25 200 e = ( − 2 ) 200 − 400 e= 200 e = −2
I = 300 x − 0.5 2
B
I = 300 x − 0.5 2
p − 300 − 0.5( 400 ) p = 300 − 200 p = 100
100 e = ( − 2) 400 − 200 e= 400 e = −0.5
= 300( 200) − 0.5( 200 ) = 60000 − 0.5( 40.000 ) = 60000 − 2000 = 40000 B I = ( 300 − 0.5 x ) x
2
I I I I
I I I I
= 300( 400) − 0.5( 400 ) = 120000 − 0.5(160000 ) = 60000 − 80000 = 40000 2
7 x = 4100 − p 2
(
x 2 = 4100 − p 2
)
2
x 2 = 4100 − p x 2 − 4100 = − p
( − 1)
x 2 − 4100 = − p( − 1)
x 2 − 4100 = p p = 4100 − x
A
B p = 4100 − x p = 4100 − 50 p = 4050
p = 4100 − x p = 4100 − 40 p = 4060
(
)
1 4060 2 e = 4100 − p 2 40 1 4060 1 2 − 2 ( 0 − 2 p ) e = 4100 − p 40 2 1 − 4060 1 e = 4100 − p 2 2 − 2 p 40 2
(
)
(
)
(
)
4060 2 e = − p 4100 − p 40 −p 4060 e = 40 4100 − p 2
−1
2
4050 e = 50 4050 e = 50
1 2 ( 4100 − p ) 2
4050 e = 50 4050 e = 50
1 1 2 − 2 ( 4100 − p ) 2 − 2 p
1 1 2 − 2 ( 4100 − p ) 2 ( 0 − 2 p )
1 2 − − p ( 4100 − p ) 2 −p 4050 e = 50 4100 − p 2
− 4060 4060 e = 40 4100 − ( 4060) 2
4050 e = 50
− 4060 4060 e = 40 4100 − 16483600 − 4060 4060 e = 40 − 16929500 4060 − 4060 e = 40 − 4057.4
4050 e = 50 4050 e = 50
4060 e = − (1) 40 − 4060 e= 40 e = −101.5
− 4050 4100 − ( 4050 )
2
− 4060 4100 − 16402500 − 4060
− 16398400 4050 − 4060 e = 50 − 4049 .4 4050 e = (1) 50 4050 e= 50 e = 81
1 C ( x) = 10 + 2 x C ( x) = 2
2 C(x) = 40 + (In2)x 2
( 2)
C(x) = 0 + (In2)(2x) + x 2 1 x2 2 12 C(x) = 2(1) In2 + 2 1 C(x) = 2In2 + 2 C(x) = 2In2 + 0,5 C(x) = 2xIn2 +
C(x) = 1,38 + 0.5 C(x) = 1,88
3 C ( x ) = 0.0001x 3 − 0.09 x 2 + 20 x + 1200 C ( x ) = 0.0001x 3 − 0.09 x 2 + 20 x + 1200 C ( x ) = 0.0003 x 2 − 0.18 x + 20 C ( x ) = 0.0003(1) − 0.18(1) + 20 C ( x ) = 0.0003(1) − 0.18 + 20 C ( x ) = 0.0003 − 0.18 + 20 C ( x ) = 19.82 2
4 C ( x ) = 10 −6 x 3 − (3 *10 −3 ) x 2 + 36 x + 2000
C ( x ) = 10 −6 (3 x 2 ) − (3 * 10 −3 ) x 2 + 36 x + 2000 C ( x ) = 30 x −4 − 30 −3 ( 2 x ) + x 2 ( 0 ) + 36 C ( x ) = 30 x −4 − 60 x −2 + 36 C ( x ) = 30(1)
−4
− 60(1)
−2
+ 36
C ( x ) = 30 −4 − 60 −2 + 36 C ( x ) = 0.0000012 − 0.00027 + 36 C ( x ) = −0.0002765 + 36 C ( x ) = 35.49
5 R ( x ) = x − 0.01x 2 R ( x ) = 1 − 0.02 x
R ( x ) = 1 − 0.02(1) R ( x ) = 0.98
6 R ( x) = 5 x − 0.01x 5 2 0.05 3 2 x 2 0.05 3 2 R( x) = 5 − (1) 2 R( x) = 5 −
R( x) = 5 −
0.05 2
3
R ( x ) = 5 − 0.025
2
3
2
= 5 − 0.0039
R ( x ) = 4.9961
7
R ( x ) = 0.1x − 10 −3 x 2 − 10 −3 x
[
5
2
]
7 5 R ( x ) = 0.1 − 10 −3 ( 2 x ) + x 2 ( 0 ) − 10 −3 5 x 2 + x 2 ( 0 ) 2 7 R ( x ) = 0.1 − 20 x −2 + 0 − 25 x 2 + 0
[
]
R ( x ) = 0.1 − 20 x −2 − 25 x R ( x ) = 0.1 − 20(1)
7
2
− 25(1)
−2
7
2
7
R ( x ) = 0.1 − 20 −2 − 25 2 R ( x ) = 0.1 − 0.0025 − 0.0000128 R ( x ) = 0.097
(
8 R ( x ) = 100 x − ( Log5) x 3 1 + x
)
R ( x ) = 100 x − 0,69 x 3 1 + x 2 1 1 2 R ( x ) = 100 − 0,69 x 3 0 + 1 2 x 2 + 1 + x 2 2,07 x 1
(
)
R ( x ) = 100 − 0,345 x
5
R ( x ) = 100 − 0,345(1) 5
2 5
(
+ 2,07 x 2 + 2,07 x 2
Q P
D
X = 100 − 4 p I = p.Q
I = p (100 − 4 P ) I = 100 p − 4 p 2 I = 100 − 8 p I = 100 − 8(1) I = 100 − 8 I = 92
2
+ 2,07(1) + 2,07(1) 2
R ( x ) = 100 − 0,345 2 + 2,07 2 + 2,07 R ( x ) = 100 − 0,69 + 4,28 + 6,16 R ( x ) = 110,651
9 x + 4 p = 100
5
5
2
5
2
)
10 Q
x + p = 10 P D x = 10 − p
x
1
2
= 10 − p
x = (10 − p ) I = p.Q
2
[ ] I = p[2(10 − p ) + (10 − p ) (1) ] I = p (10 − p )
2
2
I = p ( 20 p − 2 p ) + (10 − p ) I = 20(1) − 2(1) + (10 − 1) 2
2
2
I = 20 − 2 2 + 9 2 I = 20 − 4 + 81 I = 97
11
x
3
2
+ 50 p = 1000
I = 16 x
3
I = 16 x
3
I = 16 x
3
I = 16(1) 3
2
= 1000(16 ) − 50(16) p
2
= 16000 − 800 p
2
− 16000 − 800 p
3
2
− 16000 − 800 p
I = 16 − 16000 − 800 p I = 64 − 16000 − 800 p I = 15936 + 800 p 2
12 10 p + x + 0.01x 2 = 700 x + 0.01x 2 = 700 − 10 p I = x + 0.01x 2 = 700 − 10 p I = 10 x + 0.1x 2 − 7000 + 100 p I = 10(1) + 0.1(1) − 7000 + 100 p I = 10 + 0.1 − 7000 + 100 p I = 10.1 − 7000 + 100 p 2
I = −6989.9 + 100 p
13 U = I − P
U = 100 P − 4 P 2 − (100 + 5 x ) U = 100 P − 4 P 2 − 100 − 5 x U = 100 − 8 P − 5 U = 95 − 8 P
14 U = I − C
( ) U = P (10 − P ) − 60 − X U = (10 P − P ) − 60 − X U = 2(10 P − P )(10 − 2 P ) − 1 U = P 10 − P 2 − ( 60 + x ) 2
2 2 2
U = 20 P − 2 P (10 − 2 P ) − 1 2
15 U = I − C U = 16 x
3
U = 16 x
3
U = 15 x
3
2
3 − 1600 + 800 P − 50 + x 2
2
− 1600 + 800 P − 50 − x
2
− 1950 + 800 P
3
2
(15 x ) 2 + 800 2 1 U = 45 x 2 + 800 2 1 U = 45 ( 25 ) 2 + 800 2 U = 823 .7 U =3
1
16 U = I − C
U = 10 x + 0.1x 2 − 7000 + 100 p − (1000 + 0.1x 2 ) U = 10 x + 0.1x 2 − 7000 + 100 p − 1000 − 0.1x 2 U = 10 x − 8000 + 100 p
A U U U U
B = 10 x − 8000 + 100 p = 10 (100 ) − 8000 + 100 p = 1000 − 8000 + 100 p = 7000 + 100 p
U U U U
= 10 x − 8000 + 100 p = 10 x − 8000 + 100 (10 ) = 10 x − 8000 + 1000 = 10 x − 7000
17 F (u ) = 95 − 8 p
F (u ) = 95 − 8( 0 ) F (u ) = 95
0 = 95 − 8 p p = 95 − 8 p = 87
18 F (u ) = 20 p − 2 p 2 (10 − 2 p ) − 1
F (u ) = 20( 0 ) − 2( 0 ) (10 − 2( 0 ) ) − 1 F (u ) = 0 − 2( 0) (10 − ( 0 ) ) − 1 2
F (u ) = 10 − 1 F (u ) = 9
0 = 20 p − 2 p 2 (10 − 2 p ) −1 0 = 20 p − 20 p 2 + 4 p 3 −1 0 = 20 p − 20 p 2 + 3 4 p 3 −1 0 = 20 p − 20 p + 4 p −1 0 = 4 p −1 p = 4 −1 = 3
19 p1 = 4 Q1 = 100 p 2 = 5 Q 2 = 80 p 2 − p1 Q 2 − Q1 5−4 m= 80 − 100 1 m= − 20 m = 0.005 m=
p − p1 = m( Q − Q1)
p − 4 = 0.05( Q − 100 ) p − 4 = 0.05Q + 5 p = 0.05Q + 5 + 4 p − 0.005Q − 4 = 5 p − 0.05Q = 9 0.05Q = 9 − p 9− p Q= 0.05
I = P.Q 9 − P I = P 0.05 9P − P 2 I = 0.05 0.05( 9 − 2 P ) − 9 P − P 2 ( 0 ) I = 0.05 2 0.05( 9 − 2 P ) − 0 I = 0.025 0.45 − 0.1 I = 0.025 0.45 − 0.1 I = 0.025 0.35 P= 0.0025 P = 140
20
P1 = 1 P 2 = 1.50 Q1 = 20000 Q 2 = 45000 1.50 −1 M = 15000 − 20000 0.50 M = = 0.0001 − 5000 P − P1 = M ( Q − Q1) P −1 = 0.0001( Q − 2000 ) P −1 = 0.0001Q + 2 P = 0.0001Q + 3 P + 0.0001Q = 3 3−P 0 = 1 P 0.0001
3P − P 2 0.0001 0.0001( 3 − 2 P ) − 3P − P 2 ( 0 ) 0= 0.00001 2 0.003 − 0.0002 P 0= 0.0000001 U = I − [CF + ( CV .Q ) ] 3P − 2 P U = − [10000 + ( 0.80Q ) ] 0.0001 3P − 2 P U = −10000 − 0.80Q 0.0001 0.0003 − 0.002 P U = − 0.80Q 0.0000001 0.0003 − 0.002 P 0= − 0.80Q 0.0000001 0.0003 − 0.0002 P= − 0.80Q 0.0000001 P = 10000 − 0.80 0=
P = 9999..2
A U U U U U
B 3P − P 2 = −10000 − 0.80Q 0.0001 3(1.80 ) − 1.80 2 = − 10000 − 0.80Q 0.0001 5.4 − 3.24 = −10000 − 0.80Q 0.0001 2.16 = − 10000 − 0.80Q 0.0001 = 11600 − 0.80Q
21 C ( x ) = AX
2
C ( x ) = 2 AX
U U U U U
C 3P − P 2 = − 10000 − 0.80 Q 0.0001 3(1.90 ) − 1.90 2 = − 10000 − 0.80 Q 0.0001 5.7 − 3.61 = − 10000 − 0.80 Q 0.0001 2.09 = − 10000 − 0.80 Q 0.0001 = 10900 − 0.80 Q
+ BX + C 2
+B
+ BX + C X AX 2 BX C C’ ( x ) = + + X X X C C’ ( x ) = AX + B + X AX C’ ( x ) =
AX
2
AX + B + C X 2 AX 2 + 2 AXB + 2 AXC + AXB + B 2 + BC C’ ( x ) = X 2 ZX + 2 ZXC + ZXB + B 2 + BC C’ ( x ) = X C’ ( x ) =
22 NO ES VERDAD PORQUE NO TODS LAS VARIABLES QU ESTAN ELEVADAS ESTAN MULTIPLICANDO A LA X
23
C ( F ) = 4 + 0.36 I + 0.48 I 1.44 2 4 C ( F = 0.36 ) + I 4 ∆S + ∆C = ∆I
3
4
∆S = ∆I − ∆C ∆S = 16 − 4 + 0.36 I + 0.48 I ∆S = 16 − 4 = 12 ∆S = 16 − 0.36 = 15.64 ∆S = 16 − 0.15 = 15.52 ∆S = 12 − 15.64 I − 15.52 I ∆S = 15.64 +
46.56 4
3
4
3
4
3P − P 2 − 10000 − 0.80 Q 0.0001 3( 2 ) − 2 2 = − 10000 − 0.80 Q 0.0001 6−4 = − 10000 − 0.80 Q 0.0001 2 = − 10000 − 0.80 Q 0.0001 = 10000 − 0.80 Q
U = U U U U
TALLER No. 10
1
p dx e = x dp p dx e = x p dp
p 2 0( 0 ) − ( k )(1) x P2 2 p 0−k e= 2 x p e=
x p2 − xp 2 e= xp 2 e = −1 e=
p2 x
2 A x x x x
= 500(10 − p ) = 500(10 − 2 ) = 500( 8) = 4000
2 e = [500(10 − p ) ] 4000 2 e = [500( − 1) − (10 − p )( 0) ] 4000 2 2 e = ( − 500 + 0) = ( − 500 ) 4000 4000 − 1000 e= 4000 e = −0.25
B x x x x
= 500 (10 − p ) = 500 (10 − 5) = 500 ( 5) = 2500
5 e = [ 500 (10 − p ) ] 2500 5 e = [ 500 ( − 1) − (10 − p )( 0 ) ] 2500 5 5 e = ( − 500 + 0 ) = ( − 500 ) 2500 2500 − 2500 e= 2500 e = −1
C
x = 500 (10 − p ) x = 500 (10 − 6 ) x = 500 ( 4 ) x = 2000
5 e = 2000 5 e = 2000
[ 500 (10 − p ) ]
[ 500 ( − 1) − (10 − p )( 0 ) ] 5 5 e = ( − 500 + 0 ) = ( − 500 ) 2000 2000 − 30000 e= 2000 e = −1.5
3 A x = 400 − 100 p
x = 400 − 100 (1) x = 400 − 100 x = 300 p dx e = x dp 1 e = ( 400 − 100 p ) 300 1 e = ( − 100 ) 300 − 100 e= 300 e = −0.33
B x x x x
= 400 − 100 p = 400 − 100( 2 ) = 400 − 200 = 200
2 e = ( − 100 ) 200 − 200 e= 200 e = −1
C x x x x
= 400 − 100 p = 400 − 100( 3) = 400 − 300 = 100
3 e = = −100 100 − 300 e= 100 e = −3
4 A x p + =1 1000 8 x 2 + =1 1000 8 x + 0.25 = 1 1000 x = 1 − 0.25 1000 x = 0.75(1000 ) x = 750 p 2 p ( 0 ) − 8(1) e = 1 − ( 0 ) − 1000 8 82 750 2 8 e = 0 + 1000 750 64 8 2 e = 1000 − 64 750 2 63992 e = 750 64 2 e = ( 999875) 750 1999.75 e= 750 e = 2.66
B x 4 + =1 1000 8 x + 0.5 = 1 1000 x = 1 − 0 .5 1000 x = 0.5(1000 ) x = 500 4 e = ( 999875) 500 3999.5 e= 500 e = 7.9
C x 4 + =1 1000 8 x + 0.5 = 1 1000 x = 1 − 0 .5 1000 x = 0.5(1000 ) x = 500 4 e = ( 999875) 500 3999.5 e= 500 e = 7.9
5 x = 250 − 30 p + p 2
x = 250 − 30(12 ) + 12 2 x = 250 − 360 + 144 x = 34
(
12 e = 250 − 30 p + p 2 34 12 e = ( 0 − 30 + 2 p ) 34
)
12 e = ( − 30 + 2 p ) 34 − 360 + 24 p e= 34 − 360 + 24(12 ) e= 34 − 360 + 288 e= 34 e = −2.11 Cambio Porcentual en la demanda e= Cambio Porcentual en el Pr ecio CPD = ( CPP )( e ) CPD = ( 8.5% )( − 2.11) CPD = −17,935%
6 A p p p p
= 30 − 0.5 x = 30 − 0.5( 200 ) = 300 − 100 = 200
p = 300 − 0.5 x p + 0.5 x = 300 0.5 x = 300 − p 300 − p x= 0.5 200 300 − p e = 200 0.5 200 0.5( 0 − 1) − 300 − p ( 0 ) e = 0.5 2 200
A I = ( 300 − 0.5 x ) x
200 0.5( − 1) e = 200 0.25 200 e = ( − 2 ) 200 − 400 e= 200 e = −2
I = 300 x − 0.5 2
B
I = 300 x − 0.5 2
p − 300 − 0.5( 400 ) p = 300 − 200 p = 100
100 e = ( − 2) 400 − 200 e= 400 e = −0.5
= 300( 200) − 0.5( 200 ) = 60000 − 0.5( 40.000 ) = 60000 − 2000 = 40000 B I = ( 300 − 0.5 x ) x
2
I I I I
I I I I
= 300( 400) − 0.5( 400 ) = 120000 − 0.5(160000 ) = 60000 − 80000 = 40000 2
7 x = 4100 − p 2
(
x 2 = 4100 − p 2
)
2
x 2 = 4100 − p x 2 − 4100 = − p
( − 1)
x 2 − 4100 = − p( − 1)
x 2 − 4100 = p p = 4100 − x
A
B p = 4100 − x p = 4100 − 50 p = 4050
p = 4100 − x p = 4100 − 40 p = 4060
(
)
1 4060 2 e = 4100 − p 2 40 1 4060 1 2 − 2 ( 0 − 2 p ) e = 4100 − p 40 2 1 − 4060 1 e = 4100 − p 2 2 − 2 p 40 2
(
)
(
)
(
)
4060 2 e = − p 4100 − p 40 −p 4060 e = 40 4100 − p 2
−1
2
4050 e = 50 4050 e = 50
1 2 ( 4100 − p ) 2
4050 e = 50 4050 e = 50
1 1 2 − 2 ( 4100 − p ) 2 − 2 p
1 1 2 − 2 ( 4100 − p ) 2 ( 0 − 2 p )
1 2 − − p ( 4100 − p ) 2 −p 4050 e = 50 4100 − p 2
− 4060 4060 e = 40 4100 − ( 4060) 2
4050 e = 50
− 4060 4060 e = 40 4100 − 16483600 − 4060 4060 e = 40 − 16929500 4060 − 4060 e = 40 − 4057.4
4050 e = 50 4050 e = 50
4060 e = − (1) 40 − 4060 e= 40 e = −101.5
− 4050 4100 − ( 4050 )
2
− 4060 4100 − 16402500 − 4060
− 16398400 4050 − 4060 e = 50 − 4049 .4 4050 e = (1) 50 4050 e= 50 e = 81
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