## Determination of Optimum Route Connecting Two Locations |

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2CSQ assumed calculated Calculus of Variations catenary ci+1 ci+i computations connecting two points constant cost lines construction cost contour cost contour lines convergent corresponding branches corresponding point cost factor cost function cost per mile defined Definition determined equation 2-UO estimation Euler-Lagrange Euler-Lagrange equation expression flow f flow factor geometrical given Hence I+To illustrated improvement increment intersect iterative procedure Lagrangian multipliers least cost path least cost route Linear Programming mathematical induction matrix minimized minimum cost path obtained optimization optimum route P0 to Pn parameters partial derivatives path from P0 polygons problem Proof of Theorem represented result route connecting Section 2-3 segments sequence series xij simplified small number solution solving straight line subareas subsection Substituting system of equations T+Tm Theorem VI Theorem VIII transportation costs variable terrain vector