Question-3: (Flexible Machine System - Machine Selection Problem) A Flexible Manufacturing System consists of 2-Automatic-MachineTools used for the manufacture of 7-Jobs. Both the machines have a tool-slot holder / pallet-holder, of a circular form as shown in the figure. There is a limitation of the total number of tools which may be fixed on the tool-slot holder. A table given below mentions the processing time of a job on a particular type of machine. There are 7Jobs to be processed on the 2-Machines. The number of tools required for a particular job is shown in the row Si, which indicates the number of tools required for each of the Jobs J1 to J7 on any of the machines. It may be noted that the tool used by a job is not 2 common to other jobs, in other words the tool slot variable si represents a DisjointSet. Calculate an optimum schedule for this machine-loading problem, given the processing times of the two machines. The Jobs are to be assigned to a particular machine such that the Makespan is minimized. Processing Times and the Tool-requirement for the Seven-Jobs Statement of optimization: Minimize: u; where u=u1+u2 The real valued functions u1 and u2 are the processing times on the Machine M1 and M2 respectively and are stated as: u1=p11X11+p21X21++p71X71u2=p12X12+p22X22++p72X72 Here Xij=0,1 are the decision variables indicating the particular machine loading. Here, u stands for the machine loading in terms of the Makespan, pi1 and pi2 indicates the processing times on machine 1&2 respectively, and Xi1 and Xi2 are the binary decision variables of loading the machine 1&2 with the part- i. It may be noted that X11&Xi2 are mutually exclusive, hence if machine- 1 is to be loaded with the part- i the machine-2 is not to be loaded with the same part. State the Minimum value of Makespan required