Which of the following are true and which are false? explain your answers.

(i) there exists an lp with exactly two optimal solutions. (ii) there exists an lp with exactly two optimal corner solutions. (iii) if an lp is feasible, then it has an optimal solution that is a corner point. (iv) consider an lp with m constraints and n variables. we can transform it into an equivalent lp in standard form with at most 2m + 2n constraints and 2n + m variables.