$3.[10$ points$]$ Weighted $\backslash ($ A$^\{*\}\backslash )$ search is used to find a travel path between the start city and the goal city in a travelling problem. The cost function used is distance travelled. A value of $1\mathrm{.}4$ is used for $\backslash ($ W $\backslash )$ and straight line distance to the goal is used as the heuristic function $\backslash ($ h$($n$)\backslash ).$

$($a$)$ With a value of $1\mathrm{.}4$ for $\backslash ($ W $\backslash ),$ does weighted $\backslash (\backslash$mathrm$\{$A$\}^\{*\}\backslash )$ search guarantee optimal solution for the travelling problem?

$($b$)$ If your answer to $($a$)$ is No$,$ how much worse, in the worst case, is the solution found by weighted $\backslash (\backslash$mathrm$\{$A$\}^\{*\}\backslash )$ when compared to the optimal solution?