Suppose that you are given an optimization problem as: Maximize F(x), where F(x) is a function of the decision variable x. That is, there are no constraints and there is a single decision variable. Explain your answers to the following questions. (F(x) can be linear or nonlinear)
a) Can a local maximum be a global minimum? Yes or No? Explain your answer.
b) Can a local minimum be greater than a local maximum? Yes or No? Explain your answer.
c) Is a global maximum always greater than every other local maximum?