Tarea 4 Evaluaci n

Tarea 4, Hernández Santiago Viridiana.
Evaluación de Proyectos

The Johnson Company´s marketing officials report to the company´s chief executive officer that the demand curve for the company´srobots in 1996 is:
Q = 30,000 - 40P Función de la Demanda
TC= 3000 + 1/2,000*Q^2 Función de costo
Utilidad = Ingreso- Costo; Ingreso= Demanda*PrecioI=Q*P

At what price must the company sell the robots to get the maximun profit?
Get the graphic solution too.
Despejando de la ec. 1, "P", tenemos: P=-Q/40+30000/40=-Q/40+750
TR=P*Q
----->TR=Q(-Q/40+750)= -Q^2/40+750Q
MR=dTR/dQ
------>
MR=-Q/20+750
MR=MC; MC=d(TC)/dQ=Q/1000


-Q/20+750=Q/1000
dónde Q=14705.88
y
P=382.3529412
n= elasticidad=40*(P/Q)




En la siguiente tabla se hace un resumen yen amarillo se selecciona la mejor opción de precio.
X(Q)
Y (P)
MR
TR
TC
MC
Elasticidad
Utilidades
28000
50
-650
1400000
395000
28
0.071428571
1005000
26000
100
-1225
2600000
341000
26
0.1538461542259000
24000
150
-1125
3600000
291000
24
0.25
3309000
22000
200
-1025
4400000
245000
22
0.363636364
4155000
20000
250
-925
5000000
203000
20
0.5
4797000
18000
300
-825
5400000
165000
18
0.6666666675235000
16000
350
-725
5600000
131000
16
0.875
5469000
15800
355
-715
5609000
127820
15.8
0.898734177
5481180
15600
360
-705
5616000
124680
15.6
0.923076923
5491320
15400
365
-695
5621000
121580
15.40.948051948
5499420
15200
370
-685
5624000
118520
15.2
0.973684211
5505480
15000
375
-675
5625000
115500
15
1
5509500
14800
380
-665
5624000
112520
14.8
1.027027027
5511480
14760
381
-663
5623560111928.8
14.76
1.032520325
5511631.2
14720
382
-661
5623040
111339.2
14.72
1.038043478
5511700.8
14680
383
-659
5622440
110751.2
14.68
1.04359673
5511688.8
14640
384
-657
5621760
110164.8
14.64
1.0491803285511595.2
14600
385
-655
5621000
109580
14.6
1.054794521
5511420
14400
390
-645
5616000
106680
14.4
1.083333333
5509320
14200
395
-635
5609000
103820
14.2
1.112676056
5505180
14000
400
-625
5600000...