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The solution space of a single equality constraint

We start our investigation regarding the geometrical representation of 2-var linear constraints by considering first constraints of the equality type, i.e.,


It is a well-known result that, assuming tex2html_wrap_inline1549 , this equation corresponds to a straight line with slope tex2html_wrap_inline1551 and intercept tex2html_wrap_inline1553 . In the special case where tex2html_wrap_inline1555 , the solution space (locus) of Equation 9 is still a straight line perpendicular to the tex2html_wrap_inline1457 -axis, intersecting it at the point tex2html_wrap_inline1559 . Notice that the presence of an equality constraint restricts the dimensionality of the feasible solution space by one degree of freedom, i.e., it turns it from a planar area to a line segment.

UAL Data
Fri Jun 20 15:03:05 CDT 1997