$\backslash$table$[[$Qurstice$,1,2,3],[$Caurse Lesming Oatocere,$1\mathrm{.}2\mathrm{.}3,3\mathrm{.}4\mathrm{.}5,4\mathrm{.}5\mathrm{.}6],[$Grade$,\frac{?}{30},\frac{?}{40},130]]$

$(30)[ta)$ Cansi$3$er the circalatice given below. Decompose this circulation iuro fionrs alrog directed cycles. Dram the residusl network and wee the tregative cycle oprimality coodition to check whether the flow is on optimal sell$-$ive of the $=$ coot Bow problem.

$(40$ pts$)$ Use the shortest augmenting path algorithm to solve the maximum flow problem in the network below: