Reconsider the facility location problem of Example $3\mathrm{.}2,$ but now assume that the response time from point $($x$0,$ y$0)$ to point $($x$1,$ y$1)$ is proportional to the road travel distance $|$x$1$ x$0|+|$y$1$ y$0|.$

$($a$)$Find the location that minimizes average response time. Use the five$-$step method, and model as a multivariable unconstrained optimization problem.

$($b$)$Examine the sensitivity of the optimal location to the estimated number of emergencies in each $22$mile sector. Can you draw any general conclusions?

$($c$)$Comment on the robustness of this model. Compare the optimal location to that obtained in the analysis of Section $3\mathrm{.}2.$ What do you think would happen if we assumed that response time was proportional to the straight$-$line