- #1
drawar
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Homework Statement
Consider the LP:
max [itex]\, -3x_1-x_2[/itex]
[itex]\,\,[/itex]s.t. [itex]\,\,\,\,[/itex] [itex]2x_1+x_2 \leq 3[/itex]
[itex]\quad \quad \ -x_1+x_2 \geq 1[/itex]
[itex]\quad \quad \quad \quad \ x_1,x_2 \geq 0[/itex]Suppose I have solved the above problem for the optimal solution. (I used dual simplex and get (0,1) as the optimal solution.)
Now if the first constraint [itex](2x_1+x_2 \leq 3)[/itex] is either changed to
(1) max [itex]\, (2x_1+x_2,0) \leq 3[/itex], or
(2) max [itex]\, (2x_1+x_2,6)\leq 3[/itex],
is it possible to obtain the new optimal solution without having to solve the entire problem from the scratch?
Homework Equations
The Attempt at a Solution
I have tried introducing a new variable t to address the maximum and rewrite the constraints in linear form but it doesn't seem to help.Any hint or comment is greatly appreciated, thank you!