3. (25 points) Consider the following problem min f(r), s.t. r ER, where f(x) = maxi=1...,m(a; r - b;). Let v be the optimal objective cost which is assumed to be finite. Let A be the matrix with rows af , ..., a,, and b be the vector with components b1, ..., bm. . (5 points) Formulate the above problem as a linear program formulation. . (7 points) Consider any vector p E Im that satisfies p A = 0,p 2 0, and Lizpi = 1. Show that -p"b