(a) In k-means, we attempt to find k cluster centers Hje Rdj e {1,...k} and n cluster assignments clo) e {1,...,k), i E {1.... n}, such that the total distance between each data point and the nearest cluster center is minimized. In other words, we attempt to find ...and (1).....m) that minimizes 12 J(cm) = 11:0) - Mecell? To do so, we iterate between assigning to the nearest cluster center and updating each cluster center H, to the average of all points assigned to the jth cluster. Instead of holding the number of clusters k fixed, one can think of minimizing the objective function over , c, and k. Show that this is a bad idea. Specifically, what is the minimum possible value of Jer, ko)? What values of c, , and k result in this value