I have been giving the following question
Consider the following problem with alternative constraints:
max $2x_1-79x_2$
subject to $0\le x_1\le 20, 0\le x_2 \le 30$
and at least one of the following inequalities holds:
$-2x_1+3x_2\ge0$ (1)
$5x_1-4x_2\ge0$ (2)
$7x_1+8x_2\le40$ (3)
Formulate this problem as an integer programming problem.
My answer to this is
max $2x_1-79x_2$
subject to
$0\le x_1\le 20, 0\le x_2 \le 30$
$2x_1-3x_2\le M_1 (1-y_1)$
$4x_2-5x_1\le M_2(1-y_2)$
$7x_1+8x_2-40\le M_3 (1-y_3)$
$\sum^3_{j=1}y_j\ge1$
$y_j\in \{0,1\}$ for $j=1,2,3$
Choose $M_j$ so ignored constraints will not be binding.
Is this an acceptable answer? Have I made any mistakes? If yes, where abouts? Thank you:)
Yes, this is correct so far, but you should use the bounds on $x$ to make the choices of $M_j$ explicit.