- (Cowen) Solve the following problem by the simplex method:

Minimize -3*x*_{1}- 2*x*_{2}- 4*x*_{3}subject to

*x*_{1}+*x*_{2}+ 2*x*_{3}≤ 4

2*x*_{1}+ 3*x*_{3}≤ 5

2*x*_{1}+*x*_{2}+ 3*x*_{3}≤ 7

*x*_{1},*x*_{2},*x*_{3}≥ 0 - The following linear program was discussed in class (and in HW1, Exercise
2): minimize -3
*x*_{1}- 2*x*_{2}subject to*x*being nonnegative and

-2*x*_{1}+*x*_{2}≤ 1

*x*_{1}≤ 2

*x*_{1}+*x*_{2}≤ 3

Convert it to standard form and answer the following questions for each vertex:

Which other vertices (if any) could the simplex method go to from that vertex?

Which other vertices could you go to in a single pivot?