An iterative procedure yielding a nonnegative fixed point associated with the LP problem, maximize $( {x,c} )$ where $x \in \Lambda = \{ { x |Ax = b,x\geqq \theta } \}$, is developed. This procedure uses a perpendicular projection matrix formed from A, b, c, and $A^\dag $ (the Moore–Penrose–Bjerhammer generalized inverse of b). A class of linear programming problems is considered for which $A^\dag $ and related projection matrices can be obtained explicitly. This class of problems includes the Hitchcock–Koopmans transportation problem and certain of its multidimensional extensions as special cases.