Naughty cats and ruined carpets

[RockingLobstering]

My cat is ruining our lovely new carpet!
Two doors that lead into the kitchen, carpet all around. Lovely little cat, about 9 months old, has an unhealthy obsession with kitchens and climbing on worktops. He also eats everything under the sun. Tears into loaves of bread, through the foil cat food pouches, eats veg, chocolate (that one time he ate my slice of birthday cake!) So you get the idea. Worming up to date ect, so it's just his rudeness! The other cat is as good as gold
So obviously we close the kitchen doors.
Unfortunately every morning we come down he's ripped more carpet up from the doors, in a desperate attempt to get into the kitchen!
So please help us keep some of our lovely new carpet intact! Any ideas?

Leave the kitchen door open but clear all surfaces of food? Is that possible?

I have one like this, she is 16!!!
The furniture is covered in throws, she hates leather so doesn't go for the leather sofa but dear God the stair carpet is bald.
I have just had an idea, I am going to buy a large scratching post and cover it in carpet - a large piece she has scratched to death and then renew the stair carpet so it doesn't smell of her.
I've also clipped her long claws.
I'm hoping this will work.
if it doesn't the stair carpet will have to stay like that untill she dies.