Consider the following optimization problem: min:8x1+12x2+16x320x424x528x6s.t.:x1+3x2+3x3=5x4+x5+x6100xi9i=1,,6 where the variables of the multivariable optimization problem are integers. Use Extension-2 type approach, (i.e., Treat the multiple variables together as one structure or as one vector). Answer the following: (a) Let [4,5,3,1,1,1]T be the current solution. Ignore Constraints (2) \& (3), and write all the possible feasible immediate neighbors (star neighbors or unit neighbors) of the current solution. (b) Let [4,5,3,1,1,1]T be the current solution. Ignore Constraints (2) \& (3), and write 3 possible feasible extended neighbors of the current solution. (c) Execute one full iteration of the greedy search with the immediate/star neighborhood. Use starting solution as [3,0,1,1,1,1]T. Handle Constraint(2) \& (3) by creating a penalized objective function. Assume all the penalty coefficients are equal to 1000 . (d) Execute 3 full iterations of the random-walk search with the extended/expanded neighborhood. Use starting solution as [3,0,1,1,1,1]T. Handle Constraint(2) \& (3) by creating a penalized objective function. Assume all the penalty coefficients are equal to 1000 . Use random numbers from the random number table. See explanation at the end of this HW for generating random numbers. (e) Execute 4 iterations of the simulated annealing with following parameters: Initial temperature be 1000 , and starting solution be [3,0,1,1,1,1]T. Neighborhood type = Extended neighborhood, Move type = Random walk, Pool size =1, Max \# tries =4. Cooling mechanism = After 2 iterations (irrespective of success or failure in the iteration), reduce the temperature to 500 , and continue with the remaining iterations. Handle Constraint(2) \& (3) by creating a penalized objective function. Assume all the penalty coefficients are equal to 1000 . (f) Execute one next iteration of the tabu search with following parameters: Current solution = [3,0,1,1,1,1]T. Neighborhood type = Immediate neighborhood, Move type = Greedy move, Tenure period =6, and the current tabu list is: {[4,0,1,1,1,1]T,[3,0,2,1,1,1]T,[3,2,1,1,1,1]T,[3,0,1,2,1,1]T,[3,0,1,2,1,1]T,[3,0,1,1,1,2]T} The Constraint(2) \& (3) were handled by creating a penalized objective function, where all the penalty coefficients are equal to 1000