$($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 at the main building of Baruch College. We are looking for restaurants in NYC five boroughs. If we care about 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 sure Pareto efficient $($or Pareto optimal$)$ choices?

N

The cheapest restaurant in NYC$.$

Y

The closest restaurant among all those with price between $$17$ and $$25$ and rating of at least $4\mathrm{.}2.$

N

The highest rated restaurant among all restaurants in the Upper East Side with price at most $$20.$

N

A restaurant that minimizes "price $-2*$rating$".$

Y

A restaurant that minimizes "price $+$ rating $+3*$ distance".

N

The closest Italian restaurant.

Y

The highest rated restaurant with price below $$30$ and within a distance of $1$ mile.

N

The cheapest restaurant with rating at least $4\mathrm{.}6.$