Problem 2: Consider the following linear program: max 2 1 + 2 X1,12 ER 1 - ( 4) 2 1 + subject to X 2 + DC 2 20 2 1. Make a figure that illustrates the feasible set in R2. 2. Provide some integers n, m E R and matrices c E R", A E Rmx", and b E RM such that it is in standard form maxTER cox s.t. Ax = b and x > 0. 1 3. On your figure, identify each vertex x E R2 and its corresponding basis (possibly more than one) B of the columns of A so that N = 0 where N = {1, ..., n} \\ B. 4. Solve the linear program using the simplex algorithm in tableau form. Report the iterations on your figure. 5. Use the dual simplex algorithm in order to find a solution if the constraint x1