(Solved): 1. Consider the following maximization LP problem in an equational form: Maximize f(x1,x2,x3 ...

1. Consider the following maximization LP problem in an equational form: Maximize $$f\left(x_1,x_2,x_3,x_4\right)=x_1?x_2$$, subject to $$\begin{array}{r}?x_1+4x_2+x_3=18\\ 4x_1?x_2+x_4=18\\ x_1,x_2,x_3,x_4?0\end{array}$$ - What are the matrix $${\mathbf{A}}^s$$ and vectors $${\mathbf{c}}^s$$ and $$\mathbf{b}$$ of this formulation? - Verify that matrix $${\mathbf{A}}^s$$ has rank 2 (system of linear equations is consistent). - Write an initial Tucker tableau for this problem. Hint: Do not introduce any additional variables, you just need four variables already presented. - Using pivot transformations find all (both feasible and infeasible) basic solutions of this problem. Hint: $$\left(\begin{array}{l}4\\ 2\end{array}\right)=6$$ - Report all feasible basic solutions. Is there any optimal solution?