We model the area allocation decision problem for a fixed size crop farm under random yields and prices for a risk-averse farmer. We assume that in the short run, the variable input expenses are fixed per hectare and per crop (an assumption that is motivated by our data). Therefore the cost function depends only on the non-stochastic area allocation. The first order conditions of the model involve integrals across functions of random variables that do not in general have closed form solutions. Numerical simulation techniques are used to calibrate the parameters of the cost function. The two sources of randomness, price and yield, are combined into a single random variable, the yield-in-value. Based on examination of panels of yield-in-value data, we assume independence across the yield-in-value distributions and that the farmers know these distributions. We have modeled the sugar quota constraint, the Common Agricultural Policy subsidies and set-aside, and one Agri-Environmental Measure called "buffer zone".