Linear Algebra and Its Applications · Problem 8.3.14

Linear Programming and Game Theory — Gilbert Strang

Mathematics · linear-programming-cone-alternative

Problem

A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}

, describe the cone of nonnegative combinations of the columns. If

b

lies inside that cone, say

b = (3,2)

, what is the feasible vector

x

? If

b

lies outside, say

b = (0,1)

, what vector

y

will satisfy the alternative?