$3.(\backslash (\backslash$mathbf$\{40\}\backslash )$ points$).$ SMART.

A$-$ Andrea is house hunting with her husband, Bill. They are both $28$ years old, have no children, and have a combined income of $\backslash (\backslash$$ $110,000\backslash )$ per year. After looking at over $50$ houses, they have narrowed their choices down to $4$ located in the towns of Maynard, Stow, Hudson, and Bolton. The parameters that are important to them are commute, price, school system, and availability of good local Chinese food. After much soulsearching and discussion, they are able to construct the following table rating each option on each attribute $($for Schools and Chinese Food, the ratings are on a subjective $0-10$ scale; $10$ is best and $0$ is worst$)$:

Andrea and Bill feel that $\backslash (\backslash$$ $250,000\backslash )$ would be a terrific price for a home while $\backslash (\backslash$$ $550,000\backslash )$ would be terrible; they also feel that a $50-$mile commute would stink but a $5-$mile commute would be wonderful. Use the SMART technique to determine which house Andrea and Bill should buy, given the following relative weights: Commute: $15,$ Price: $20,$ Schools: $10,$ Chinese Food: $25.$ You must show all work and calculations.

B$-$Now suppose that Andrea and Bill want to consider their priorities after reflection, Their updated importance structure is as follows; price is four times as important as Chinese food, schools is three times as important as Chinese food, while school is twice as important as Commute and finally Chinese food is still somewhat important but less so than before.

Given this new relative importance structure, answer the following question.

$3-$B$-1-$Which housing option would now rank highest for them, and why?

$3-$B$-2-$How much does it differ from their decision in part $3.$A$.$

Support your responses with calculations.