1. Given the following optimization problem Minimize f(3) = (x1 - 1)2 + (x2 - 1)2 subject to g(x) = x1 + x2 - 150 92() = x120 (a) Plot the constrained optimization problem, including contours for F=1, F=4, F=9, F=16. Identify the constraints and the feasible region. Using the plot, identify the optimum. (b) Plot the pseudo-objective function contours F=1, F=4, F=9, F=16 for the exterior penalty function method when R=1. Identify the minimum of the pseudo- objective function on the plot. (C) Plot the pseudo-objective function contours F=1, F=4, F=9, F=16 for the exterior penalty function method when R=10. Identify the minimum of the pseudo- objective function on the plot. (d) Plot the pseudo-objective function contours F=1, F=4, F=9, F=16 for the exterior penalty function method when R=100. Identify the minimum of the pseudo- objective function on the plot. (e) Using the initial point(0, 0), perform two cycles of exterior penalty function. For n-D unconstrained optimization use DFP. (f) Using the initial point (1, -1), perform two cycles of interior penalty function (using the inverse penalty). For n-D unconstrained optimization use DFP. (g) Using the initial point (0, 0), perform two cycles of linear extended interior penalty function method. For n-D unconstrained optimization use DFP. (h) Using the initial point (0, 0), perform two cycles of the augmented lagrangian method presented in class. For n-D unconstrained optimization use DFP. 1. Given the following optimization problem Minimize f(3) = (x1 - 1)2 + (x2 - 1)2 subject to g(x) = x1 + x2 - 150 92() = x120 (a) Plot the constrained optimization problem, including contours for F=1, F=4, F=9, F=16. Identify the constraints and the feasible region. Using the plot, identify the optimum. (b) Plot the pseudo-objective function contours F=1, F=4, F=9, F=16 for the exterior penalty function method when R=1. Identify the minimum of the pseudo- objective function on the plot. (C) Plot the pseudo-objective function contours F=1, F=4, F=9, F=16 for the exterior penalty function method when R=10. Identify the minimum of the pseudo- objective function on the plot. (d) Plot the pseudo-objective function contours F=1, F=4, F=9, F=16 for the exterior penalty function method when R=100. Identify the minimum of the pseudo- objective function on the plot. (e) Using the initial point(0, 0), perform two cycles of exterior penalty function. For n-D unconstrained optimization use DFP. (f) Using the initial point (1, -1), perform two cycles of interior penalty function (using the inverse penalty). For n-D unconstrained optimization use DFP. (g) Using the initial point (0, 0), perform two cycles of linear extended interior penalty function method. For n-D unconstrained optimization use DFP. (h) Using the initial point (0, 0), perform two cycles of the augmented lagrangian method presented in class. For n-D unconstrained optimization use DFP