If you know MA 114 or finite math pretty well and could help me with a problem I'd really appreciate it... just pm me... I have the answer but Ihave no clue how to get it and I have the final tomorrow... appreciate any help

12/8/2005 12:18:24 AM

post the question on here

12/8/2005 12:47:05 AM

Three FM radio stations (A, B, and C) are competing for customers in the same market area. Through an aggressive advertising campaign, station A is capturing 11% of station B's customers and 5% of station C's customers each month, while losing only 2% of its customers to B and 2% to C each month. And 1% of B's customers switch to C and 1% of C's customers switch to B each month. This gives you all the information you need to set up the Markov chain for this situation.

Initially A and B each have 30% of the listeners and C has 40%

What percentage will radio station A have in the long run?


What percentage will radio station B have in the long run?


What percentage will radio station C have in the long run?


thats all but like I said... I do have the answers since the webassign is past due its .6396 for A, ..1261 for B and .2342 for C.... but I dont know how to get the answer and the final is tomorrow and I know this is going to be on them

12/8/2005 12:56:23 AM

To set the problem up; Let A1,B1,C1 be the #of customers and, Ao,Bo,Co be the initial number of customers.

From the first statement

Quote :

"station A is capturing 11% of station B's customers and 5% of station C's customers each month, while losing only 2% of its customers to B and 2% to C each month."

Because A is gaining 11%of B and 5%of C we get ( the __ means unknown placeholder)
A1= __Ao+0.11Bo+0.05Co, but we know that A is losing a total of 4%of it's customers so we know,

A1=0.96Ao+0.11Bo+0.05Co

From the same quote above we know that B and C are getting 2% of A, so we write

B1=0.02Ao+__Bo+__Co
C1=0.02Ao+__Bo+__Co

Now from the last bit of info

Quote :

"And 1% of B's customers switch to C and 1% of C's customers switch to B each month."

We get
B1=0.02Ao +__Bo +0.01Co
C1=0.02Ao+0.01Bo+__Co

We still need to get the last two pieces, so Remember the Columns must add to 1.

A1=0.96Ao+0.11Bo+0.05Co
B1=0.02Ao +__Bo +0.01Co
C1=0.02Ao+0.01Bo+__Co

So we must have,
A1=0.96Ao+0.11Bo+0.05Co
B1=0.02Ao +0.88Bo +0.01Co
C1=0.02Ao+0.01Bo+0.94Co

Now this sets up the Markov process. I have never taken Finite math so I don't know what tools you have to get A_infinity. I would use the eigen decomposition.

Here is the Matlab output to prove this is right...

>> A=[0.96,0.11,0.05;0.02,0.88,0.01;0.02,0.01,0.94]

A =

0.9600 0.1100 0.0500
0.0200 0.8800 0.0100
0.0200 0.0100 0.9400

>> A^10000

ans =

0.6396 0.6396 0.6396
0.1261 0.1261 0.1261
0.2342 0.2342 0.2342

>>

12/8/2005 2:19:25 AM