Study the below data.

Product $=$ P$101,$ P$201,$ P$401,$ P$301,$ P$501,$ P$701,$ P$001,$ P$601$

Increase in total sales percentage compared to previous financial year $=2,5,8,25,3,10,6,6$

Popularity $($result of a customer survey$)=$ Yes, Yes, Yes, Yes, No$,$ Yes, No$,$ Yes

Increase in profit percentage compared to previous financial year $=5,12,15,-5,-2,10,3,2$

Apply the EM algorithm for only $1$ iteration to partition the given products into K$=3$ clusters using the K$-$Means algorithm using only the features increase in sales and increase in profit.

Initial prototype: P$101,$ P$501,$ P$601$

Distinguish the expectation and maximization steps in your approach. Depict the responsibility Matrix & the new centroids of the clusters.

Use Manhattan distance wherever applicable.