Question $5$ to Question $10$ is based on this problem:

Solve the following LP model graphically.

Max: $4$X$1+6$X$2$

Subject to:

$2$X$1+3$X$2<=12$

$3$X$1+1$X$2<=9$

X$1+$ X$2>=2$

X$1+$ X$2<=10$

X$1,$ X$2>=0$

What is the optimal solution?

Group of answer choices

D$.$

$(4,0)$

B$.$

$(2\mathrm{.}14,2\mathrm{.}57)$

C$.$

$(3\mathrm{.}32,1\mathrm{.}8)$

A$.$

$(3,2)$

Flag question: Question $6$

Question $63$ pts

Which is not an extreme point $($i$.$e$.$ corner point$)$ of the feasible region?

Group of answer choices

C$.$

$(0,4)$

B$.$

$(6,0)$

D$.$

$(0,2)$

A$.$

$(3,0)$

Flag question: Question $7$

Question $73$ pts

What is point $(3,3)?$

Group of answer choices

D$.$

interior point

B$.$

boundary point

A$.$

extreme point

C$.$

infeasible point

Flag question: Question $8$

Question $83$ pts

Which is the redundant constraint?

Group of answer choices

X$1+$ X$2<=10$

B$.$

$3$X$1+1$X$2<=9$

A$.$

$2$X$1+3$X$2<=12$

C$.$

X$1+$ X$2>=2$

Flag question: Question $9$

Question $93$ pts

Which is the tight constraint? $($Tight constraint means the boundary line of the constraint intersects at the point where the optimal solution is located$)$

Group of answer choices

D$.$

X$2>=0$

A$.$

$2$X$1+3$X$2<=12$

B$.$

X$1+$ X$2>=2$

C$.$

X$1+$ X$2<=10$