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assumed boundary line catenary Cicitl citl computations connecting two locations connecting two points constant cost lines construction cost contour lines convergent corresponding branches corresponding point cost factor cost function cost per mile defined Definition degree equation determined developed differential Ex+ bf expression flow f flow factor geometrical given Hence illustrated improvement increment intersect iterative procedure l-ll Lagrangian multipliers larger than zero least cost path least cost route Let Xil linear linear programming mathematical induction matrix minimized minimum cost path mixi Newton's Method obtain optimization optimum route connecting parameters partial derivatives Pi—l polygons problem Proof of Theorem represents result Section 2-3 segments sequence series xij simplified small number solution solving subareas subsection Substituting system of equations Theorem VI Theorem VIII TRANSPORTATION UNIT COST variable terrain vector см