Consider the linear program minimize z = −5x¹ − 7x² subject to −3x¹ + 2x² ≤ 30 −2x¹ + x² ≤ 12 x¹, x2 ≥ 0. 

(i) Draw a graph of the feasible region. 

(ii) Determine the extreme points of the feasible region. 

(iii) Determine two linearly independent directions of unboundedness. 

(iv) Convert the linear program to standard form and determine the basic feasible solutions and two linearly independent directions of unboundedness for this version of the problem. Verify that the directions of unboundedness satisfy Ad = 0 and d ≥ 0