Question 7 1. Using the relationship between primal and dual problems, test if the solution (0.25, 0.25,0) is optimal for the following LP: Minimise Z = 12x1 + 8x2 + 8x3 1, 23 subject to: 4x1 + 4x2 + 4x3 > 2 3x1 + x2 X3 > 1 X1, X2, X3 20 2. Given the primal objective Maximise Zp 6x1 + 8x2 and a feasible solution (5,5), if the X1, X2 dual objective is Minimise Zp = 300y1 + 110y2 with a feasible solution of (0.2,0.8), find Yu, Y2 an upper bound and a lower bound for the objective value of the primal problem. Explain your answer. 3. Suppose that variable x; leaves the basis at some iteration p. Explain why it is not possible that X; enters the basis at the end of iteration p + 1