calculation puzzle - A tour of 36 cities

Each of 4 people is touring 36 cities separately. Each of the 36 squares in the illustration below represents a city. To make the answers shorter, each city has been given a 1-character name, from A-Z, and 0-9

Note: Although this puzzle is possible to solve without computer programming knowledge, it's allowed and encouraged to use computer help.

Each city has been rated in the following 4 areas. The ratings go from -5 to 5.

A tour must include each of the 36 cities exactly one time, start at city A, and end at city 4. Each move must be either horizontal or vertical, along the small roads that connect the cities.

As the tour progresses, all of the ratings of previously-visited cities accumulate (are added together) for each of the four categories to produce four total scores- one for each of the four categories. For example, going from A to B would leave the person feeling a -9 (-4 + -5) for Money-making Potential for city B, and a 0 (-5 + 5) for Overall Happiness for city B. Then, moving from B to C, Money-making Potential is now at -11, and Overall Happiness is at -2.

Find four tours

1. 
   

   Monroe believes that money is the root of all evil. Find him a tour such that one or more cities on that tour minimize his Money-making Potential. What is his favorite city (or cities) on that tour?

   
   


2. 
   

   Hal is focused almost solely on being happy. Find him a tour such that one or more cities on that tour maximize Overall Happiness. What is his favorite city (or cities) on that tour?

   
   


3. 
   
   

   Rose is into romance. Find her a tour such that one or more cities on that tour maximize Romance & Love. What is her favorite city (or cities) on that tour?

   
   


4. 
   

   Arlene is an admirer of artistic beauty. Find her a tour such that one or more cities on that tour maximize Art & Architecture. What is her favorite city (or cities) on that tour?

   
   

Here is an example of a valid tour:
ABCDEFLKJIHGMNOPQRXWVUTSYZ0123987654

Answer

Here are two routes that I believe maximize happiness for Hal

A B H G M S Y Z 0 1 2 W V U T N O I C D J P Q K E F L R X 3 9 8 7 6 5 4

A B C D J I H G M S Y Z 0 1 2 W V U T N O P Q K E F L R X 3 9 8 7 6 5 4

These routes both generate 23 happiness in city V

And here is a route that should maximize Art for Arlene

A G M S Y Z 0 U T N O P Q K J I H B C D E F L R X W V 1 2 3 9 8 7 6 5 4

This route generates 24 Art at cities J and I