- #1

CarmineCortez

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## Homework Statement

The question is "Show that in the case of any linear program, every convex combination of optimal extreme points is optimal."

## Homework Equations

ok so if (x_1,...,x_n) is a list of the optimal points then

a_1(x_1)+ ...+a_n(x_n) is the convex combination st a_i>0 and sum of a's is 1

so the convex combination spans the list of optimal points.

their dimensions are the same so the convex combination is a basis for the optimum points...

## The Attempt at a Solution

is this the right idea, i don't see how to show EVERY convex combinaiton is optimal