If instead the objective function of the above problem is found to be Maximizez = 3x1x2 + 6x; and the constraints are unchanged, which of the following statements is true about the objective function of this new maximization nonlinear program? (3 marks) The objective function is convex. The objective function is concave. The objective function is neither convex nor concave. The objective function is both convex and concave. 6. How many Lagrange multipliers should be introduced for the KKT conditions of the new maximization nonlinear program mentioned in Question 5? (3 marks) None of the above. 7. For the Lagrange multipliers mentioned in Question 6, which of the following statements is true? (3 marks) O All the Lagrange multipliers are non-negative. O All the Lagrange multipliers are non-positive. O Some of the Lagrange multipliers are non-negative, while the other Lagrange multipliers are non-positive. O None of the above.8. For the KKT conditions mentioned in Question 6, how many equations are of the form (Lagrange multiplier)X(corresponding constraint function) = 0? (3 marks) None of the above. 9. x1= 0,x2 =3, x3 = 0 is a solution to the KKT conditions mentioned in Question 6. (3 marks) True False Consider the following linear program Maximize z = -3x1 - X2 + 6x3 subject to - 2 1 + 2 + 523 2 -4 x1 +2+ 23