Problem-3: A manufacturing system was originally laid out for facilitating mass production with Functional Manufacturing layout. There are in total 7-Machines and 8-Part Families being produced in the manufacturing unit. The seven machines were laid out to assist the Functional Manufacturing and are denoted as machine M1 to M7. The part-families being manufacture are denoted as P1 to P8. The layout of the machines and parts are denoted conventionally by an incidence matrix given below: P1 P7 P8 INCIDENCE MATRIX Part Families P2 P3 P4 P5 P6 1 1 1 1 1 1 1 1 1 1 1 1 M1 M2 M3 M4 M5 M6 M7 Machines 1 1 1 1 1 1 1 The incidence matrix is a binary matrix and the entries are unity where the parts visit the machine as shown above, therefore the part-P1 visits the machine M3 hence the entry in the corresponding cell of M3-P1 is 1. If the part does not visit a particular machine then the entry is left blank. Use the Rank Order Clustering method to cluster the incidence matrix which will be suitable for Cellular Manufacturing. Hence calculate the following: (1) Work out the weights for ordering the Machines using the 2's exponents; (ii) Reorder the machines by sorting the weights in descending order; (iii) Next work out the weights for the Part Families adopting the same method; (iv) Reorder the Part Families by sorting the weights; (v) Hence work out the Cellular Manufacturing layout: (vi) Indicate which machines are going to be part of which cell and which Part Families will be manufactured in those cells