A manufacturing facility has $7$ machines that process $8$ different products. Below is the Process Flow Analysis $($PFA$)$ matrix showing the machine$-$part relationships. The company wants to implement cellular manufacturing to improve workflow efficiency. Using the Rank Order Clustering method: a$)$ Form the machine cells and product families $($show all calculation steps$)$ b$)$ List which machines and parts are assigned to each cell c$)$ Are the resulting product families mutually exclusive? If not, what options are available to ensure parts can be processed completely within their assigned cells?