Let S denote a subset of R and define its convex hull as Conv(S) := XER...

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Let S denote a subset of R" and define its convex hull as Conv(S) := XER" x = \;s; where , S1, .. Sp S, 1, . . ., p 0, and and 11+ i=1 1+...+\p = 1. +p Assume that the set S is finite with p elements and let x = Conv(S). Say we want to find a convex combination that maximizes - 2 + 3 .. p. Can we do this using linear programming? Let S denote a subset of R" and define its convex hull as Conv(S) := XER" x = \;s; where , S1, .. Sp S, 1, . . ., p 0, and and 11+ i=1 1+...+\p = 1. +p Assume that the set S is finite with p elements and let x = Conv(S). Say we want to find a convex combination that maximizes - 2 + 3 .. p. Can we do this using linear programming?