The linear programming problem

Question 1

standard maximisation problem

Answer 1

max z=c^T x
subject to Ax<=b
x>= On

Question 2

standard minimisation problem

Answer 2

min z=c^T x
subject to Ax>=b
x>=On

Question 3

canonical (maximisation) problem

Answer 3

max z=c^T x
subject to Ax=b
x>=On

Question 4

convex set

Answer 4

for all x,y in S and λ in [0,1], λx + (1-λ)y in S

Question 5

closed convex set

Answer 5

includes boundaries

Question 6

hyperplane

Answer 6

(n=/ On) H = {x in R^n : n^T x=d}

Question 7

positive/negative closed half-plane

Answer 7

{x in R^n : n^T x>/<=d}

Question 8

closed polyhedron

Answer 8

intersection of closed half-spaces