1.3 In some step of simplex algorithm to solve a linear programming problem with decision variables X1, X2, we have the following tableau: Z X1 X2 S1 S2 Basic RHS Ratio variables 1 0 0 0 6 6 17 0 1 -7 34 1 1 0 1 1 (a)(3 points) Find the current basic feasible solution (BFS) and put in above table. Is current BFS in one of the four cases: (i) the unique solution, (ii) alternative solutions, (iii) infeasible, and (iv) unbounded? In which case? (b)(4 points) If your answer is case (i), please write the optimal solution and the objective value; If your answer is case (ii), please first find another optimal solution in a new tableau, and then write down the expression for all possible solutions of X1, X2; If your answer is case (iii) or (iv), give the reason. 1.4 (6 points) The following linear programming problem has no feasible solution. min 0x4 + 0x2 s.t. x1 + x2 40 (3) x1,x220 Assume that we have the penalty cost $10 for failing to satisfy 1 unit of 10 in the 1st constraint; the penalty cost $5 for failing to satisfy 1 unit of 15 in the 2nd constraint; the penalty cost $1 for failing to satisfy 1 unit of 40 in the 3rd constraint. Please add some deviational variables on these three constraints to formulate this problem as a goal programming problem to minimize the penalty cost (just write a linear programming model with explanations on new variables)