We introduce a modification of the quadratic-Leontieff multi-output cost function that is particularly suitable for the data of the Farm Accountancy Data Network. We present least squares and entropy estimates of that function and compare their results for a sample of crop farms. Our results are encouraging for the use of entropy estimators in cases in which farms are not assumed to share the same technology. Our approach can be seen as an extension of the Positive Mathematical Programming approach (Howitt, 1995). The extension consists in an explicit specification of inputs in the cost function and in the possibility of modeling several farms simultaneously.