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.

Solve the problem by using a venn diagram a group of students were surveyed about their taste in music.they were asked how they like three types of music: rock, country western and jazz.the results are summarized below: no one dislikes all three types of music.six like all three types of music.eleven don’t like country western.sixteen like jazz.three like country western and jazz, but not rock.six don’t like rock.eight like rock and country western.seven don’t like jazz.how many students were surveyed?