Persona vs Product, The new chicken & egg?

We all are familiar with the riddle of chicken and egg. With so much contradictory information flying around, I wonder which one should come first, persona or the idea of a product ?
Persona is an arch typical character build in order to guide the designing of the product. In my opinion creating a persona is the logical thing to do because it is not realistic to use feed back from real users for every step of the process. Life style facts varies hugely from one person to another, so it is impossible to design a product that satisfy the needs of each and every individual. When creating a persona we try to identify the most generalized characteristics from a group of people.
However this does not mean we should create a random persona without having a clue about the product. Of course, back in the day so-called "inventors" might have blindly observed human lives with the hope of an eureka moment. But in today's fast moving world, with limited resources available one cannot afford to waste time in search of such eureka moments. Therefore it is more productive if the product-designer could first define an area (of human lives) that he wants to concentrate on.
For example, with our project, we started by deciding who we want to target with our product: People over sixty. This was followed by a primary brainstorming - session identifying possible products. At this stage we started creating persona, incorporating different aspects of older people's lives. Then more refined products were identified with the guidance of the persona created. Next these persona needs to be refined to exaggerate the particular aspects that are more crucial for our product.(You can follow the progress of our project from other entries)
My point is that the idea of having a persona followed by a product design or vice versa is neither productive nor pragmatic. Instead these two processes should be parallel and they should complement each other.