$($Enter$$Y$$for Pareto$-$optimal solutions$$and$$N$$for the non$-$Pareto$-$optimal ones.$$Questions are graded automatically. If you do not follow the formatting, then your answer will be graded wrong. If your answer is correct, I will be able to manually change your grade for those questions later, but you will lose $25\%$ of the points. NO EXCEPTIONS, in order to be fair to everyone in the class.$)$

We are in Washington Square Park. We are looking for Japanese restaurants in NYC five boroughs. If we care about three objectives, namely, the price $($menu price$),$ quality $($Yelp rating$),$ and the distance $($according to Google map$)$ of the restaurants in NYC$,$ which of the following restaurants are for guaranteed to be Pareto efficient $($or Pareto optimal$)$ choices?$$

The highest rated Japanese restaurant in NYC$.($Y$/$N$?)$

The cheapest Japanese restaurant in Soho with rating at least $4\mathrm{.}3.($Y$/$N$?)$

The highest rated Japanese restaurant with price below $$30$ within a distance of $1$ mile. $($Y$/$N$?)$

The closest Japanese restaurant among all those with price at most $$40$ and rating between $4\mathrm{.}0$ and $4\mathrm{.}5.($Y$/$N$?)$

A Japanese restaurant that minimizes "price $+4*$distance$".($Y$/$N$?)$

A Japanese restaurant that minimizes $"2*$price $+3*$rating$".($Y$/$N$?)$

A Japanese restaurant that maximizes $"10*$rating $-$ price". $($Y$/$N$?)$

The highest rated Japanese restaurant with a backyard, a rating of at least $4\mathrm{.}5,$ and a distance of at most $3$ miles. $($Y$/$N$)$