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MAE9: Homework #7, Fall 2006
Due on Thursday, November 9, before 9:00 pm
In void prob1(void), predict the market fractions of three dairies A,
B, C (i = 0, 1, 2) that supply all the milk consumed in Rosie Town.
We assume that the overall number of customers in the town N does not
change.
The initial fractions of the total market on December 31 is
shown by x0[], i.e., the dairies A, B, C have, respectively, {0.2,
0.3, 0.5} of the market. Let the transition matrix [A] be shown by
a[][], where a[i][i] = fraction of i's customers, x0[i], retained by i
and a[i][j]= fraction of j's customers, x0[j], that switch to i (if i
!= j).
Then, the market fractions on January 31 is obtained by
{x1}
= [A]{x0}. For example, in January the dairy A retains a fraction
a[0][0] of its own customers and attracts a fraction a[0][1] of B's
customers and a[0][2] of C's. Assuming that the transition matrix does
not change, predict the market fractions at the end of February,
March, April, .
.., December. Print the results for each month using