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I have the following linear program. All I've done is added my slack variables (w) and made each constraint the subject, as you do.

[itex]\mathrm{maximize} \ z=x_1+3x_2 \

w_1 = -3 + x_1 + x_2 \\

w_2 = -1 + x_1 - x_2 \\

w_3 = 4 - x_1 -2x_2[/itex]

This seems a rather silly question, but I was lead to believe that I need to run the phase one method if the linear program is infeasible - ie, if either if the objective z value is completely negative (so we can't improve on it) or if I can't find an initial basis to start the simplex algorithm.

However, in this case, can't I let [itex]x_2[/itex] enter, then as a result, [itex]w_3[/itex] is my pivot row so [itex]w_3[/itex] leaves so we can now start with the simplex?

I have no idea why the latex isn't working... I've added new lines but it certainly isn't cooperating.

http://imageshack.us/m/51/7668/phasei.png

This is what I meant.

(I've also not really followed the template since... well, it's not really an actual homework, more of a passing query, and I can't really attempt a query :P )