The linear program Max $31+22$ is solved subject to the constraints i$)x1+x210$ ii$)31+x224$ iii$)x1+2216$ and iv$)$ non$-$negativity for both $x1$

and X$2.$ After solving the linear program, the objective function coefficient for $x2$ is changed from $2$ to a new value $C2$ and the objective function coefficient fo

$x1$ is changed from $3$ to a new value $C1.$ Now the linear program is re$-$solved. Which of the following statements is true?

The new optimal solution switches to the point $(4,6)$ as long as $C110.$

The new optimal solution value is $40$ as long as $C25.$

The new optimal solution must occur now at $(8,0)$

The new optimal solution remains at $(7,3)$ as long as $-3-C\frac{1}{C}2-1.$The linear program Max $3$X$1+2$X$2$ is solved subject to the constraints i$)$ X$1+$ X ii$)3$X$1+$ X iii$)$ X$1+2$X and iv$)$ non$-$negativity for both X$1$ and X$2.$ Which of the following statements is true? The optimal solution occurs at the point $(6,6).$ The optimal solution occurs at $(8,0)$ and the optimal value is $24.$ The optimal solution value is $41.$ The feasible region has five corner points.