In this paper a quadratic programming problem is considered. It contains, as special cases, formulations of constrained matrix problems with unknown row and column totals, and classical spatial price equilibrium problems with congestion. An equilibration algorithm, which is of the relaxation type, is introduced into the problem. It resolves the system into subproblems, which in turn, can be solved exactly, even in the presence of upper bounds. Also provided is computational experience for several large-scale examples. This work identifies the equivalency between constrained matrix problems and spatial price equilibrium problems which had been postulated, but, heretofore, not made.