Compute the following:

Three clients of Disruptd 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