# Too much of a good thing - examples of production (or utility) functions that are initially increase in a factor and then decrease

I'm attempting to build a spatial model that estimates labour distributions after climate change impacts agricultural production. The key point to note is that some rainfall is good, and some temperature is good, but only up to a point - too much rain will drown the plants, and too hot a temperature will cause them and the soil to lose moisture too quickly.

In the model, I use the data I have to calibrate and get values for productivity in the context of the model, and I would like to use those estimates to estimate the parameters of some production function, so that to run the counterfactual, I can apply projections of climate data to estimate productivities in each country. Does anyone know of production functions with the required property?

$$F(R,T)=100000-(R-200)^2-(T-25)^2,$$
where $$F$$ is production (in kg), $$R$$ is rainfall in a year (in mm), and $$T$$ is average temperature over the course of a year (in °C).
This says that under the optimal growing conditions of $$R=200$$ and $$T=25$$, production will be 100,000 kg.
If rainfall $$R$$ or temperature $$T$$ is higher or lower than these optimal levels, then production will be lower than 100,000 kg.