Consider the following Linear Program: max 2x1 +x2 s.t . x1 =0: (a) Write down the dual of the LP. (b) (15 points) Suppose we

Consider the following Linear Program:

max 2x1 +x2

s.t . x1 <=3;

x1 +x2 <= 5;

2x1 - 3x2 0;

x1 >= 0; x2>=0:

(a) Write down the dual of the LP.

(b) (15 points) Suppose we know that x = (3; 2) is an optimal solution to (LP). Use complementary slackness conditions to find the set of all optimal solutions to the dual of (LP).