If I have a linear programming problem e.g. $$\max 2x_1 + x_2$$ with these constraints
$$x_1-2x_2 \leq 14$$ $$2x_1-x_2\leq 10$$ $$x_1-x_2 \leq 3$$
And I want to solve the problem starting from a specific point e.g. $A=(x1=5, x2=0)$ and $B=(x1=0, x2=5)$ .
How should I configure the initial tableau to allow to iterate simplex method starting from these points?
(Note that in standard form when I add the slack variables, the points must be calculated in function of the extra variables.)
One way would be, for a start at (5,0), to set up a new variable $x_1'$ and put the original $x_1$ equal to $5+x_1'$ in the objective and constraints. Then the usual simplex, starting at $(0,0)$ in the $x_1',x_2$ variables, would in effect be starting at $(5,0)$ in the $x_1,x_2$ variables.