Solve Problem w/ Two Phase Method: Max Z

[peteryellow]

CAn somebody please help me that how can I solve the following problem with two phase method

maximize z = x_1 - 9x_2
subject to
x_1 +3x_2 +2x_3 =< 12
2x_1 + 2x_3 = 14
5x_1 +3x_2 +8x_3 = 50
x_1 >= 0, x_2>= 0, x_3>= 0.

 

[HallsofIvy]

That's a "linear programming" problem, right?

Max or min of a linear function, over a convex polygon, will occur at a vertex. Here, however, two of the "inequalities" are actually equations.

Find the point at which the planes x_1+ 3x_2+ 2x_3= 12, 2x_1+ 2x_3= 14, and 5x_1+ 3x_2+ 8x_3= 50 intersect.

 

[peteryellow]

yes but I have to solve it by using two phase method