Practical Economic Analysis and Computation in Six Optimization Models

Economic interpretation of the Karush–Kuhn–Tucker (KKT) mathematical theory leads to practical economic analysis in the context of convex quadratic production planning models of a multiplant firm with and without capacity constraints. Necessary and sufficient optimality conditions help in correcting common mistakes of intuitive economic reasoning. I demonstrate that ranking of plants by Marginal Cost at Start of Production (MCSP) helps in developing an algorithm for the problem without capacity constraints. And for the problem with capacity constraints, the Marginal Cost at Full Production (MCFP) for every plant is also relevant for algorithm development. Algorithmic proof for an equivalence theorem is another novel contribution. I develop the best possible algorithm for sensitivity analysis deriving a mapping between System Marginal cost and satisfiable demand.