A recursive production function
The min operation is known as a Leontief production function http://en.wikipedia.org/wiki/Leontief_production_function

You're right that with Leontief production functions, the equilibrium is always aE=uK, which is to say that production is linear, and factors are consumed in fixed proportion. There are some real world examples for this: to drive, for example, you need a car and wheels in an exact 1:4 proportion, and having 6 wheels per car doesn't let you produce anything more than 4 wheels per car. But for the most part the aim is just to motivate a linear approximation to a multi-sector economy, which we can easily plug into a computer and run economy-wide computations with. We didn't have high powered computers in those days (c. 1950), so computing multi-sector non-linear production technologies was simply out of the question.