A question about solving a linear program using the Tableau Method

[Hells_Kitchen]

I am trying to solve the following linear program using the tableau method:

Max Z = 25X1 + 100X2 subject to:
0.10X1 – 0.90X2 + S1 = -10
0.85X1 – 0.15X2 + S2 = -15
0.60X1 + 0.60X2 + S3 = 40
X1 , X2 , S1 , S2 , S3 ≥ 0

The feasible region is just a triangle but the origin is not contained in it.

I would like to set up the first tableau but I have to start from a feasible extreme point.

I have picked Point (50,16.67) which corresponds to S3=S1=0, but I cannot complete the whole tableau:

Basis--Z--X1--X2--S1--S2--S3---Value----Ratio

Z-----1---0---0----?---0---?-----2917
X1----0---1---0----?---0---?-----50
X2----0---0---1----?---0---?-----16.67
S2----0---0---0----?---1---?----- -25


Does anybody have any clues? Thanks.

 

[fresh_42]

I'm not really fit in the Simplex algorithm, but you could change coordinates such that the origin is a vortex of the feasible set.