Calcium etc has a big part to play on egg production and quality (calcium and certain vitamin deficiencies can cause shelless eggs, or weak eggshells, and less taste to the egg, etc) a good way to go is give them enough food in the AM for them to eat it all in about 10 minutes, and again in the evening.
If you want egg layers get them from a hatchery or hatchery stock, they will definately lay 4+ eggs a week. A breeder/show line bird is going to have poorer egg production, the breed wasn't meant to be an egg layer and breeders/showers breed true to the breed where a hatchery breeds the better egg layers and their aim is egg producers for themselves and consumers. Only drawback is the best looking birds are show line birds. Dont get me wrong, most hatchery birds have the big crests as well.
The picture you have up is a ROOSTER, the HENS have a much nicer poofy crest that sits neat on the head. the rockstar look is for the boys only.