Use and the result of problem 3.7 to prove the following. For every LP problem Problem 3.7 Prove that for every pair of expressions in (3.5) there is a positive number b such that the following two...

Use and the result of problem 3.7 to prove the following. For every LP problem

Problem 3.7

Prove that for every pair of expressions in (3.5) there is a positive number b such that the following two statements are equivalent: (i) r is lexicographically smaller than s; (ii) for every choice of numbers e₁,e₂,. , e_n, such that

r is numerically smaller than s.