What is the basic economic problem?

In economics the main problem we deal with is the fact that there is a finite number of resources on the planet. In other words we don't have an unlimited amount of things. e.g. we will eventually run out of oil and gas.

What are the implications of this? 3 questions come to mind:

1. What to produce with only limited resources?

So for example how much food should be produced? 

2. How to produce?

What factors of production should be used. Should labour be used or machines. How much should be used. 

3. Who should we produce for? 

How doe we distribute these goods that we have made. Should we give goods and services to those who can pay more? or should we use a different allocative system?

The study of economics tries to grapple with these questions through the use of models. These models help us simplify the real world in order to be able to make judgements and predictions; hopefully allowing us to answer some of these questions.