Connsider the linear programming problem Max $z = 5x_1 + 6x_2$ st. $10x_1 + 3x_2 \leq 52,2x_1 + 3x_2 \leq 18$ and $x_1, x_2 \geq 0$ and integer.
How would one manipulate the resources so that the existing optimal solution remains feasible yet $x_1$ becomes an integer? For those familiar I was considering using the Gomery cutting plane method, but am not sure how to be certain the result is the new optimal solution. Further, this is part of a series of questions that then ask me to use a cutting plane that targets $x_1$ and makes it into an integer. Why would these give different solutions?