S:= ={vere: 320}. (b) Consider the set X1 + 2x2 + 3x3 + 4x4 1, x3 > X1 2x2 + x3 Express the set S as the feasible region of an LP with three constraints using the same variables X1, X2, X3, X4. Prove that your formulation is correct. (c) Let n > 2 be an integer and consider the LP with n2 variables X11, X12, ... , Xnn: maximize 0 subject to {j=1 lij 1 Vi E {1, 2, ..., n} 1 Vj E {1, 2, ..., n} Xij > 0, Vi, je {1, 2, ...,n}. Show how to express the feasible region of this LP as the solution set of {i=1 lij Ax 0, where x := [211, X12, Inn]T, A has 2n rows and n2 columns and b is 2n-by-1. Describe A and b in terms of the data for the original LP. Prove all your claims. S:= ={vere: 320}. (b) Consider the set X1 + 2x2 + 3x3 + 4x4 1, x3 > X1 2x2 + x3 Express the set S as the feasible region of an LP with three constraints using the same variables X1, X2, X3, X4. Prove that your formulation is correct. (c) Let n > 2 be an integer and consider the LP with n2 variables X11, X12, ... , Xnn: maximize 0 subject to {j=1 lij 1 Vi E {1, 2, ..., n} 1 Vj E {1, 2, ..., n} Xij > 0, Vi, je {1, 2, ...,n}. Show how to express the feasible region of this LP as the solution set of {i=1 lij Ax 0, where x := [211, X12, Inn]T, A has 2n rows and n2 columns and b is 2n-by-1. Describe A and b in terms of the data for the original LP. Prove all your claims