Linear Algebra and Its Applications · Problem 8.3.3

Linear Programming and Game Theory — Gilbert Strang

Mathematics · linear-programming-duality-identity

Problem

Suppose

A

is the identity matrix (so that

m = n

), and the vectors

b

and

c

are nonnegative. Explain why

x^* = b

is optimal in the minimum problem, find

y^*

in the maximum problem, and verify that the two values are the same. If the first component of

b

is negative, what are

x^*

and

y^*