The Highway Slope Problem

One of the most widely used sources of problems for a mathematical modeling course is the series of modules prepared by the TEAM project at Oklahoma State University and distributed by the Mathematical Association of America. The module on Highway Slope Design [Choike 19841 considers the problem of joining two straight segments of highway in a vertical plane by a parabolic transition curve. The purpose of this note is to suggest that the first problem in that module is incorrectly posed, and to offer a more appropriate formulation of the design problem.