Lowe and Hurter introduced the "generalized market area problem" of simultaneously determining production levels and distribution patterns at n plants to satisfy demand distributed over a subset of R^k. Here we give simpler proofs and extensions of their results. We also show how the problem can...

I Brouwer’s Theorem -- II Some Applications of Brouwer’s Theorem -- III Triangulations -- IV Algorithms to Find Completely-Labelled Simplices -- V Extensions of Brouwer’s Theorem -- VI Applications of Kakutani’s Theorem and its Extensions -- VII Eaves’ First Algorithm -- VIII...