$1.$ Please solve the fractional knapsack problem. What is the maximized benefit? $(40$ points$)$

$4$ items

Max weight is $8$

Item $1$: weight $5$; benefit $7$

Item $2$: weight $2$; benefit $4$

Item $3$: weight $3$ ; benefit $5$

Item $4$: weight $4$; benefit $6$

$2.$ Please show the Huffman tree to find Huffman codes for letters $\text{'}\backslash ($ a $\backslash )\text{'},\text{'}$b$\text{'},\text{'}$c$\text{'},\text{'}$d$\text{'},$ and $\text{'}$ e $\text{'}$ in the character string 'addcebeadbadbaeddbacadceabaeddade' and decode the binary string $\text{'}0111110000100011\text{'}(60$ points$)$