Use Matlab/Python to answer the following 2 questions Q1.4 supermarkets (A, B, C
ID: 3042822 • Letter: U
Question
Use Matlab/Python to answer the following 2 questions Q1.4 supermarkets (A, B, C,D) working on advertisement to get higher market share. After several months, it is found a stable transition was established as follows 30% customers of A stay with A, 10% changes to B, 30% changes to C. and rest customers changes to D; 20% customers of B changes to A, 35% stays with B, none changes to c, and rest to D; and both C and D keep all customers. 1. 2. 3. Prepare a transition matrix, and Get the limit transition matrix. If the market share begins with A 0.3, B-0.3, C 0.15, and D-0.25, please find the stable market share. Q2. For a (6x6) transition matrix given as following, please find the limiting matrix 1.0000 0 1.0000 1.0000 0.3000 0.1000 0.2000 0.1000 0.2000 0.4000 0.1000 0.2000 0.3000.3000 0.3000 0.2000 Q3. For a (SxS) transition matrix given as following, please find the limiting matrix 1.0000 1.0000 0.3333 0.3056 0.6111 .0833 0.0000 0.0000 0 1.0000 0 0.4444 0.2222 0.0000 0.0000Explanation / Answer
A
B
C
D
A
0.3
0.1
0.3
0.3
B
0.2
0.35
0
0.45
C
0
0
1
0
D
0
0
0
1
A
B
C
D
A
0
0
0.4482759
0.5517241
B
0
0
0.137931
0.862069
C
0
0
1
0
D
0
0
0
1
From the table of P48 it is observed that eventually all customers of C and D will remain intact with it, whereas nearly 45 % customers of A will shift to C and 55 % to C. Similarly 14 % of customers of B will shift to C and 86 % to D. It means in the long run C and D will capture the complete market.
Then stable market share is as follows: This is obtained by changing TPM P with change in market share of A and it is found that P65 is
A
B
C
D
A
0
0
0.2468354
0.7531646
B
0
0
0.0759494
0.9240506
C
0
0
1
0
D
0
0
0
1
From the table of P65 it is observed that eventually all customers of C and D will remain intact with it, whereas nearly 25 % customers of A will shift to C and 75 % to C. Similarly 7.6 % of customers of B will shift to C and 92.4 % to D. It means in the long run C and D will capture the complete market.
Q2. Given 6X6 TPM P. It is found that P65 is stable distribution as shown below
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0.245614
0.3859649
0.3684211
0
0
0
0.3114035
0.5964912
0.0921053
0
0
0
0.3815789
0.4210526
0.1973684
0
0
0
Q3. Given 5X5 TPM P is as follows
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0.2222
0.4444
0.3333
0
0
0.3056
0.6111
0.08333
0
0
It is further found that Pn = P for all n. Hence given TPM itself is a limiting matrix.
A
B
C
D
A
0.3
0.1
0.3
0.3
B
0.2
0.35
0
0.45
C
0
0
1
0
D
0
0
0
1
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