A clothing manufacturer is planning to offer $2$ clothing sizes to its potential customers. Suppose that the manufacturer has the bust, waist, and hips measures of all its $6$ customers, C$1-(37,31,40),$ C$2-(35,29,38),$ C$3-(32,24,34),$ C$4-(36,28,40),$ C$5-(40,33,44),$ C$6-(33,24,36).$ Since you have learned k$-$means clustering in your data mining class, the manufacturer wants to ask you to apply the technique to determine the $2$ optimal production sizes and what size to offer to each of the $6$ customers. Suppose that the initial seeds $($centers of the clusters$)$ are C$3$ and C$5.$ Please run the k$-$ means algorithm for ONE iteration and report: $(1)$ the $2$ optimal production sizes in bust, waist, and hips; $(2)$ which of the two sizes to offer to each of the $6$ customers based on the results obtained after one iteration.