***********Please make sure that part b is explained properly step by step********

Consider the following problem: Minimize f(x1, x2) = x1 + x2 subject to: h(X): x2= x2, g(X): X1 + 2x2 > 2 a) First solve it using graphical method. b) Next, suppose we wish to solve it using a penalty function approach. First define an augmented cost function, P(X,R), by introducing suitable penalty functions for violation of the constraints. Then minimize P(X,R) as an unconstrained optimization problem. Please explain how the solutuion depends on R and how R should be chosen to reach the true constrained minimum. Consider the following problem: Minimize f(x1, x2) = x1 + x2 subject to: h(X): x2= x2, g(X): X1 + 2x2 > 2 a) First solve it using graphical method. b) Next, suppose we wish to solve it using a penalty function approach. First define an augmented cost function, P(X,R), by introducing suitable penalty functions for violation of the constraints. Then minimize P(X,R) as an unconstrained optimization problem. Please explain how the solutuion depends on R and how R should be chosen to reach the true constrained minimum