[yrnunez]

saludos a todos,

quisiera un poco de ayuda para resolver este problema que intento resolver.

A baseball team consists of 2 stars, 13 starters, and 10
substitutes. For tax purposes, the team owner must value the
players. The value of each player is defined to be the total
value of the salary he will earn until retirement. At the
beginning of each season, the players are classified into one
of four categories:

Category 1 Star (earns $1 million per year)
Category 2 Starter (earns $400,000 per year)
Category 3 Substitute (earns $100,000 per year)
Category 4 Retired (earns no more salary)

Given that a player is a star, starter, or substitute at the
beginning of the current season, the probabilities that he
will be a star, starter, substitute, or retired at the beginning
of the next season are as follows:

                                NextSeason
ThisSeason   Star    Starter   Substitute Retired
Star              0.5      0.3        0.15         0.05
Starter          0.2      0.5        0.2           0.1
Substitute      0.05    0.15       0.5           0.3
Retired           0        0            0             1

Determine the value of the team’s players

de antemano muchas gracias...

[yrnunez]

solucion,


clear
% matriz original
M = [.5  .3  .15 .05;
     .2  .5  .2  .1;
     .05 .15 .5  .3
     0   0   0   1]
 
% separacion de la matriz en parte transitoria y absorbente
Q = M(1:3, 1:3)
R = M(1:3, 4)

% matriz inversa
I = eye(3);
 
% matriz de periodos esperados : (I-Q)^(-1)
Per = (I-Q)^(-1)
 
% matriz de probabilidades : (I-Q)^(-1)*R
Prob = Per*R

Est = 1000000;  % ganancia estrella por anio
Nov =  400000;  % ganancia novato por anio
Res =  100000;  % ganancia reserva por anio

ValEst = Est*Per(1,1) + Nov*Per(1,2) + Res*Per(1,3)
ValNov = Est*Per(2,1) + Nov*Per(2,2) + Res*Per(2,3)
ValRes = Est*Per(3,1) + Nov*Per(3,2) + Res*Per(3,3)