Scientists have been giving especial attention to the estimation of variance components in mixed models in the last decades. Consequently several estimation methods have been proposed, what makes the choice of one among them difficult. It is noteworthy, however, that a significant majority of these studies have considered only models for fixed effects factors. On the other hand, in many practical situations one or more factors may be associated with processes of sampling, characterizing the factors and random effects in this context are very important random effects models and mixed-effects models. In general, three aspects are crucial in the discussion of mixed models: estimation and testing of hypotheses about the fixed effects, the prediction of the random effects and the estimation of variance components. In general both the prediction of the random effects as the estimation of fixed effects depend on the estimation of variance components. Furthermore, the estimation of variance components is made on unbalanced data, the estimate can be obtained depending on the method used. In other words, different estimation methods can lead, under imbalance, different estimates of the same parameter. Given the importance of the topic, many methods have been proposed for the estimation of variance components. Basically, are universally consecrated nine methods derived from three concepts of classical statistical estimation: the moments, the likelihood function and quadratic functions. Among the derivatives of moments methods are the method of Fisher (1918), ANOVA and methods I, II and III Henderson (1953); among derivatives of the likelihood function is the method of maximum likelihood, ML, Hartley & Rao (1967) and restricted maximum likelihood, REML, Patterson and Thompson (1971) and those derived from the estimation of quadratic functions are the methods of quadratic estimators minimum standard minquë (Rao, 1971a), minimum variance, MIVQUE (Rao, 1971b) and iterative minimum norm, I-minquë, Searle (1987).

It sounds like an optimisation problem. You need first to formulate your problem by identifying objective (s) such as maximising profit and then specifying the constraints. If you need any assistance we can discuss together. 

Look at cervero and kockelman (1997), they have used dissimilarity index and entropy index to measure the mixing of land use. I use the same concept with floor space in land area in my research.