Problem $3.$ Let $G=(V,E)$ be a graph with $n$ vertices, and $n+1$ edges.

$($a$)$ Suppose the weight of every edge of $G$ is $10.$ What is the weight of the minimum spanning

tree of $G?$

$($b$)$ Now, assume that $G$ has exactly one edge of weight $20,$ exactly one edge of weight $5,$ and the

weight of every other edge is $10.$ What are the possibilities for the weight of the MST of $G?$