Question $2$: Consider the following all integer linear programming $($ILP$)$ model.

Max $x_1+x_2$

$s.t.$

$,2x_1+2x_{2}9$

$,6x_1+x_{2}6$

$,x_{1}0,x_{2}0$ and Integer

$(2\mathrm{.}1)$ Solve the linear programming relaxation $($LPR$)$ problem graphically and obtain an

optimal solution. Show your work.

$(2\mathrm{.}2)$ Solve the original problem $($ILP$)$ graphically and obtain an optimal solution. Is it

possible to obtain the optimal solution of the ILP from the optimal solution of LPR by

rounding up or down? Justify your answer.

$(2\mathrm{.}3)$ Suppose we remove the first constraint from the above problem. Solve the LPR and

ILP problems graphically in this situation.