25 Consider the following LP:

It is given that

a Show that the basic solution with basic variables x1, x2, and x3 is optimal. Find the optimal solution.
b Write down the dual to this LP and find its optimal solution.
c Show that if we multiply the right-hand side of each constraint by a non-negative constant k, then the new optimal solution is obtained simply by multiplying the value of each variable in the original optimal solution by k.

Transcribed Image Text:

max z = 2x1 + x2 + x3 s.t. x1 + x3 1 x2 + x 2 x1 + x2| 3 x1, x2, x30