1. Consider the following standard production problem Maximize c'x s.t. Ax <= b Xi >= 0 Where A is an m by n matrix (m constraints and n variables), x is an n by 1 vector, and b is an m by 1 vector. A' is the transpose matrix of A. Its dual problem is Minimize b'y s.t. A'y c Yi >= 0 For the given primal problem below, write out the dual problem in the table. PRIMAL Maximize 3x1+5x2 Subjected to x1<= 4 (resource 1) 2x2< 12 (resource 2) 3x1+2x2<=18 (resource 3) X1, X2 >= 0 DUAL

1. Consider the following standard production problem Maximize c'x s.t. Ax <= b Xi >= 0 Where A is an m by n matrix (m constraints and n variables), x is an n by 1 vector, and b is an m by 1 vector. A' is the transpose matrix of A. Its dual problem is Minimize b'y s.t. A'y c Yi >= 0 For the given primal problem below, write out the dual problem in the table. PRIMAL Maximize 3x1+5x2 Subjected to x1<= 4 (resource 1) 2x2< 12 (resource 2) 3x1+2x2<=18 (resource 3) X1, X2 >= 0 DUAL