Problem 3 Consider the problem minimize f(x) s.t. x X where f : R² → R is given by f(x) = 3x₁ with x = (x₁, x₂)¹, and X = {x = (x₁, x₂): x₁ + x2}. Answer each of the following questions, showing complete justification. a. Does the point z* = (2,0) satisfy the FD-FONC? b. Does the point x* = (2,0) satisfy the FD-SONC? c. Is the point x* = (2,0) a local minimizer? Hint: Draw a picture with the constraint set and level sets of f.

Fig: 1