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1. A pivot in the Simplex Method is said to be degenerate when Max.Z=0.40X1+0.40X2+1.83 it doesn't change the value of the objective function; this happens when we get a ratio of 0 in choosing the leaving 0.6016.42+4.830 variable. Degenerate pivots are somewhat common, and 0.211.82+0.630 usually harmless, but in some cases are not. Professional 0.4011.62+0.230 software packages take the possibility of degeneracy into X21 account. Consider the LP problem shown at the right. all variables non-negative a) Set up the problem to be solved using the Simplex Method. Show all tables resulting from the sequence of pivot operations; verify that - if you strictly follow the simplex rules given in class - after 6 simplex iterations you are back to the original table, and consequently, the problem cycles. b) Write the dual of the given problem. Use the dual-simplex method to solve the dual problem. Show all your iterations. Does the dual also presents a similar cycling problem? Explain you answer in detail. c) Do an internet search to find out which simple changes you can make to the simplex algorithm to avoid cycling in problems that degenerate. Summarize and explain what you found out