Determine the proportions of the original customers

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Reference no: EM131813456

Question 1. Three clients of Disrup, Ltd P, Q and R are direct competitors in the retail business. In the first week of the year P had 300 customers Q had 250 customers and R had 200 customers. During the second week, 60 of the original customers of P transferred to Q and 30 of the original customers of P transferred to R. similarly in the second week 50 of the original customers of Q transferred to P with no transfers to R and 20 of the original customers of R transferred to P with no transfers to Q.

Required

a) Display in a matrix the pattern of retention and transfers of customers from the first to the second week

b) Re-express the matrix that you have obtained in part (a) showing the elements as decimal fractions of the original numbers of customers of P, Q and R

Refer to this re expressed matrix as B

c) Multiply matrix B by itself to determine the proportions of the original customers that have been retained or transferred to P, Q and R from the second to the third week.

d) Solve the matrix equation (xyz)B = (xyz) given that x + y + z = 1

e) Interpret the result that you obtain in part (d) in relation to the movement of customers between P, Q and R

Question 2. There are three types of breakfast meal available in supermarkets known as brand BM1, brand BM2 and Brand BM3. In order to assess the market, a survey was carried out by one of the manufacturers. After the first month, the survey revealed that 20% of the customers purchasing brand BM1 switched to BM2 and 10% of the customers purchasing brand BM1 switched to BM3. similarly, after the first month of the customers purchasing brand BM2, 25% switched to BM1 and 10% switched to BM3 and of the customers purchasing brand BM3 0.05% switched to BM1 and 15% switched to BM2

Required
i. Display in a matrix S, the patterns of retention and transfers of customers from the first to the second month, expressing percentage in decimal form.

ii. Multiply matrix S by itself (that is form S2)

iii. Interpret the results you obtain in part ii with regard to customer brand loyalty

Reference no: EM131813456

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1/15/2018 12:52:46 AM

FIRST ASSIGNMENT OF QUANTITATIVE METHODS. Be in group of two students. MBA PROGRAM 1. Three clients of Disrup, Ltd P, Q and R are direct competitors in the retail business. In the first week of the year P had 300 customers Q had 250 customers and R had 200 customers. During the second week, 60 of the original customers of P transferred to Q and 30 of the original customers of P transferred to R. similarly in the second week 50 of the original customers of Q transferred to P with no transfers to R and 20 of the original customers of R transferred to P with no transfers to Q. a) Display in a matrix the pattern of retention and transfers of customers from the first to the second week

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