Consider the set S = {xe {0, 1, 2):, 23, 4, 5 x1, xy = x;} and a function defined on this set given by 1: SR with f(x) = cx, where c =(4,-1,0) Further, for all xes. a neighborhood is defined as follows: N(x) = {x'ES: 3x -3x =1} {x} x Hints: The set Scomprises exactly 6 elements. The neighborhood N(x) consists of x and of all vectors in Shaving a component sum exceeding the component sum of x by exactly 1. a) (3 points) Determine all elements xes as well as the corresponding function values f(x). b) (4 points) For all elements xeS, specify the set of neighborhood solutions N(x). . a c) 3 points) Specify for each x S, which of the following statements are true: x is a local maximum with regard to N(x) x is a local minimum with regard to N(x) x is a global maximum * is a global minimum