Two mines A and B are able to extract up to $5$ and $4$ tonnes of raw materialper day, respectively, Raw material is then transported to the two factoriesC' and D$.$ Up to $4$ tonnes of raw material per day can be transported fromthe mine A to the factory C$,$ up to $2$ tonnes per day $-$ from the mine A to thefactory D$,$ up to l tonne per day $-$ from the mine B to the factory C$,$ and upto $2$ tonnes per day $-$ from the mine B to the factory D$.$ Both factories C andD are capable of processing up to $4$ tonnes of raw material per day. Use fownetworks and the Ford$-$Fulkerson algorithm to maximize the total amount ofraw material processed by the two factories. To this end, calculate:$($i$)$How much raw material per day should each of the mines A and Bextract.

$($ii$)$ How much raw material per day should be transported along