5.13 Consider the following process. Starting with a linear programming problem in standard form, n maximize cje; i=1 n subject to aijl; 0 j = 1, 2, ...,n, first form its dual: m minimize biyi i=1 m subject to yidi; 2 c; j=1,2,...,n i=1 Yi > 0 i = 1, 2, ..., 1 m. Then replace the minimization in the dual with a maximization to get a new linear programming problem, which we can write in standard form as fol- lows: maximize 19: i=1 subject to 0 i = 1, 2, If we identify a linear programming problem with its data, (aij, bi, C;), the above process can be thought of as a transformation T on the space of data defined by (aiz, bi, ci) I(aji, Cj, bi). Let 5* (aij,bi, C;) denote the optimal objective function value of the standard- form linear programming problem having data (ajj, bi, C;). By strong dual- ity together with the fact that a maximization dominates a minimization, it follows that $* (aij, bi, C;) 0 j = 1, 2, ...,n, first form its dual: m minimize biyi i=1 m subject to yidi; 2 c; j=1,2,...,n i=1 Yi > 0 i = 1, 2, ..., 1 m. Then replace the minimization in the dual with a maximization to get a new linear programming problem, which we can write in standard form as fol- lows: maximize 19: i=1 subject to 0 i = 1, 2, If we identify a linear programming problem with its data, (aij, bi, C;), the above process can be thought of as a transformation T on the space of data defined by (aiz, bi, ci) I(aji, Cj, bi). Let 5* (aij,bi, C;) denote the optimal objective function value of the standard- form linear programming problem having data (ajj, bi, C;). By strong dual- ity together with the fact that a maximization dominates a minimization, it follows that $* (aij, bi, C;)