question archive Three companies Benfel Ltd, Cromwell Ltd and Samtec Ltd were recently launched in the Kenyan market
Three companies Benfel Ltd, Cromwell Ltd and Samtec Ltd were recently launched in the Kenyan market
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Three companies Benfel Ltd, Cromwell Ltd and Samtec Ltd were recently launched in the Kenyan market. The companies have operated in the Kenyan market for a few months now. At the beginning of the month of August 2021, a survey on monthly brand switching behavior was conducted on a representative sample among customers of the three companies. The survey revealed that Benfel Ltd retains 70% of its customers and loses 20% to Cromwell Ltd and 10% to Samtec Ltd. Similarly, Cromwell Ltd retains 60% of its customers and loses 30% to Benfel Ltd and 10% to Samtec Ltd. Furthermore, Samtec Ltd retains 50% while it loses 30% to Cromwell Ltd and 20% to Benfel Ltd. It 2 has been determined that there will be 3,500, 4,300 and 2,200 customers shopping with Benfel Ltd, Cromwell Ltd and Samtec Ltd respectively at the start of the month of September 2021.
Required:
a) Formulate the transition matrix for this system (1mark)
b) Evaluate the distribution of the sample surveyed as at the beginning month of August 2021 (5 marks)
c) Compare the long run state of the market amongst the three companies (4 marks)
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Answer
Based on assumption that x, y, and z are customers of three companies in August: Benfel Ltd, Cromwell Ltd, and Samtec Ltd.
Step-by-step explanation
Explanation
A) Let x, y, z are customers of three companies Benfel Ltd, Cromwell ltd and Samtec ltd, in starting month of August.
b) Now Benfel loses 30% of its customer at the end of August and have 3500 customers.
x* 70/100 = 3500
x= 5000 customers
Similarity
Cromwell ltd loses 40% of its customers and have 4300 customers
y* 60/100= 4300
y= 7167 customers
Similarity,
Samtec ltd loses 50% of its customers and have 2200 customers
z* 50/100= 2200
z= 4400 customers
So, the conclusion is;
| Company | Customers in August | Customers in September |
| Benfel ltd | 5000 | 3500 |
| Cromwell ltd | 7167 | 4300 |
| Samtec ltd | 4400 | 2200 |
c) From the above distribution indicates clear that Benfel ltd loses minimum customers compared to Cromwell and Samtec ltd hence, Benfel ltd will grow steadily in long run while Cromwell ltd and Samtec ltd will have to face severe competition.
