Problem #1:  Cat vomits right after meals.

Suggestion:  Try putting the food dish on a box.  A common problem with cats is a flap of skin right at the entrance of the stomach.  The food is trapped and comes up when the esophagus is too full.  Raising the food dish forces the cat to eat in an upright position, opening the flap above the stomach and allowing the food to enter.

Problem #2:  Cat sheds too much

Suggestion:  Feed the cat a higher quality of cat food.  Nutrition affects many things such as temperment, litter box habits, and coat.  A high quality diet will not only improve shedding, but will also improve the texture of the coat.  I have seen this change myself.  The cat stopped shedding and her coat became softer and more shiny.

Problem #3:  A fat cat who doesn't play.

Suggestion:  You might try different toys.  Toys that make one cat's eyes sparkle can produce yawns in other cats.  A nice interactive toy is a feather teaser.  Cats enjoy feather toys because they remind cats of birds.  Or you can find a cat fishing pole which the cat can chase across the room.

Problem #4:  A wild cat that demands play all the time.

Suggestion:  Find a friend.  If your cat is receptive, you might try a dog.  But another cat around the same age would be ideal.  Don't get a tiny kitten to be a companion for a six month old.  The kitten can't take that kind of rough housing.

Problem #5:  Cat who runs around the room at top speed.

Suggestion:  Play with your cat more.  You might try chasing games.  One of my cats, Zari, enjoys being chased.  Cats invite a chase by approaching then backing off repeatedly.  Chase the cat, but don't catch it.  Let it win.