1. Consider the following linear optimization problem min 3+3: s.t. m+y=1, 350,3;30. Does this problem have an optimal solution? Is this problem feasible? Explain your answer. 2. Consider the following optimization problem min (a: - sin(:c)}2 s.t. .1: E R. (a) Find all the global minimum solutions. Explain how you nd them. Hint: there mag.r be multiple ones. (b) Is there any local minimum solution that is not a global minimum solution? {o} Is the objective function x} = (m -sin(1:)}2 a convex function on IR? 3. Consider the foIlOwing optimization problem _ 1 min 1-" s.t. .1: 2 0. Does this problem have an optimal solution? Why