we have Vertices a$(6),$ b$(5),$ c$(-3),$ d$(-4),$ e$(-4)$ with their demand$/$supply values Edges with $($lower bound, capacity$)$: b$$a: $(5,7)$ c$$b: $(1,9)$ a$$c: $(4,8)$ e$$a: $(2,5)$ a$$d: $(3,8)$ e$$d: $(1,4)$ d$$c: $(2,5)$ Your task is to determine if a feasible circulation exists in this graph by completing the following steps: $($a$)$ Remove the lower bounds on each edge. Write down the new demands on each vertex a$,$ b$,$ c$,$ d$,$ e in this order. $($b$)$ Solve the circulation problem without lower bounds. Write down the max$-$flow value. $($c$)$ Determine whether a feasible circulation exists in the original graph. Explain your answer