Equilibrio de la empresa con funciones empíricas:
|
Tn Vda. |
Precio Vta. |
CM |
|
|
ENERO |
4 |
30 |
15 |
|
FEBRERO |
6 |
15 |
35 |
|
MARZO |
1 |
60 |
30 |
|
ABRIL |
2 |
50 |
20 |
|
MAYO |
7 |
10 |
50 |
|
JUNIO |
3 |
40 |
12 |
|
JULIO |
5.5 |
25 |
25 |
PUNTO 1: Demanda. Ajuste lineal demanda
|
x |
p |
p2 |
x2 |
p x |
x* |
|
4 |
30 |
900 |
16 |
120 |
-183.41 |
|
6 |
15 |
225 |
36 |
90 |
-58.30 |
|
1 |
60 |
3600 |
1 |
60 |
-433.63 |
|
2 |
50 |
2500 |
4 |
100 |
-350.22 |
|
7 |
10 |
100 |
49 |
70 |
-16.59 |
|
3 |
40 |
1600 |
9 |
120 |
-266.82 |
|
5.5 |
25 |
625 |
30.25 |
137.5 |
-141.70 |
|
28.5 |
230 |
9550 |
145.25 |
697.5 |
-1450.67 |
a= å x * å p2 - å p * å px = 8,01
N * å p2 – (å p) 2
p= -0,12x + 8,01
b= N * å x - å p * å x = -0,12
N * å p2 – (å p) 2
r = N * å xp - å x * å p = -0,99 Desvío reducido en un 99%.-
[N * å x2 – (å x)2]1/2 * [N * å p2 – (å p)2]1/2
PUNTO 2: Costos
|
X |
Y |
X2 |
X3 |
X4 |
X2Y |
XY |
CM* |
|
|
ENERO |
4.00 |
15.00 |
16.00 |
64.00 |
256.00 |
240.00 |
60.00 |
14.34 |
|
FEBRERO |
6.00 |
35.00 |
36.00 |
216.00 |
1296.00 |
1260.00 |
210.00 |
32.88 |
|
MARZO |
1.00 |
30.00 |
1.00 |
1.00 |
1.00 |
30.00 |
30.00 |
30.05 |
|
ABRIL |
2.00 |
20.00 |
4.00 |
8.00 |
16.00 |
80.00 |
40.00 |
19.01 |
|
MAYO |
7.00 |
50.00 |
49.00 |
343.00 |
2401.00 |
2450.00 |
350.00 |
50.86 |
|
JUNIO |
3.00 |
12.00 |
9.00 |
27.00 |
81.00 |
108.00 |
36.00 |
13.78 |
|
JULIO |
5.50 |
25.00 |
30.25 |
166.38 |
915.06 |
756.25 |
137.50 |
26.07 |
|
28.50 |
187.00 |
145.25 |
825.38 |
4966.06 |
4924.25 |
863.50 |
187.00 |
å
y= a0 N + a1 å x + A2 å x2 187= a0 7 + a1 28,5 + a2 145,25å
xy= a0 å x + a1 å x2 + a2 å x3 863,50= a0 28,5 + a1 145,25 + a2 825,38å
yx2= a0 å x2 + a1 å x3 + a2 å x4 4.924,25= a0 145,25 + a1 825,38 + a2 4.966,06Usando el Método de Cramer:
|
7 |
28.5 |
145.25 |
|
|
28.5 |
145.25 |
825.38 |
15917.6 |
|
145.25 |
825.38 |
4966.06 |
a0
|
187 |
28.5 |
145.25 |
|
|
863.5 |
145.25 |
825.38 |
46.90 |
|
4924.25 |
825.38 |
4966.06 |
a1
|
7 |
187 |
145.25 |
|
|
28.5 |
863.5 |
825.37 |
-19.75 |
|
145.25 |
4924.25 |
4966.06 |
a2
|
7 |
28.5 |
187 |
|
|
28.5 |
145.25 |
863.5 |
2.90 |
|
145.25 |
825.37 |
4924.25 |
CM*= 46,90 – 19,75x + 2,90 x2
CT= CM * x
CT= 46,90x – 19,75 x2 + 2,90 x3
CMg= 46,90 – 39,5x + 8,70 x2
IT= Px = p= (-0,12x + 8,01) x= -0,12 x2 + 8,01x
Img= -0,24x + 8,01
Máx B® B’= 0 B"< 0
B’= I’ – C’= 0
Máx. B ® I’ = C’
-0,24x + 8,01 = 46,90 – 39,5x + 8,70 x2
8,70 x2 + 39,26x – 38,89 = 0 0,84
-5,.35
CT0,84 = 46,90x – 19,75 x2 + 2,90 x3 = 46,90*,084 – 19,75*0,842 + 2,90*0,84= 27,18
CMg0,84= 46,90 – 39,5x – 8,70 x2 = 46,90 – 35,90*0,84 – 8,70*0,842= 7,58
IT0,84 = -0,12 x2 + 8,01x = -0,12*,0842 +,8,01*0,84= 6,81
Img0,84 == -0,24x + 8,01 = -0,24*0,84 + 8,01= 7,80
P0,84 = -0,12x + 8,01 = -0,12 * 0,84 + 8,01= 7,90
B0,84 = 7,80 – 7,58 = 0,22
y= å y
N
r2= å (y* - y)2 Þ r= (r2
)1/2 coeficiente de correlación
å
(y - y)2|
X |
Y* |
Y |
Y |
Y- |
Y*- |
(Y- |
(Y*- |
|
4 |
14.34 |
15 |
|||||
|
6 |
32.88 |
35 |
|||||
|
1 |
30.05 |
30 |
|||||
|
2 |
19.01 |
20 |
|||||
|
7 |
50.86 |
50 |
|||||
|
3 |
13.78 |
12 |
|||||
|
5.5 |
26.07 |
25 |
|||||
|
28.5 |
187.00 |
187 |
26.71 |
160.29 |
160.29 |
25691.5 |
25691.5 |
r2 = 25691,50 = 1 Þ r= 1
25691,50