Balancing pairs of interfering elements

Many decisions in different fields of application have to take into account the joint effects of two elements that can interfere with each other. For example, in Industrial Economics the demand for an asset can be influenced by the supply of another asset, with synergic or antagonistic effects. The same happens in Public Economics, where two differing economic policies can create mutual interference. Analogously, the same is true about drugs in Veterinary Science and Medicine, additives in Agriculture, diets in Zoo-technics and so on. When it is necessary to use such elements, there is sometimes a primary interest in one effect rather than the other: for instance, the effect of one could be twice as strong as that of the other. In such cases, it is important to consider the extent of influence of the elements while deciding about the dosage of them. In this paper we provide a direct method, not an iterative one, to obtain the optimal solution of the problem. In the next section, we shall give the basic definitions and in the next three ones we will present the optimization problem and the solution method, together with its theoretical foundation. Some applications to Economics and other fields are presented in sections 6 and 7.