Consider the following linear programming model
This linear programming model has:
$$\begin{array} { l l }
\operatorname { Min } & 2 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 } \
\text { Subject to: } & \mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } \geq 4 \
& \mathrm { X } _ { 1 } \geq 2 \
& \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0
\end{array}$$
A)unique optimal solution
B)unbounded solution
C)infeasible solution
D)alternate optimal solution
E)redundant constraints

Question

Consider the following linear programming model
This linear programming model has:
$$\begin{array} { l l } 
\operatorname { Min } & 2 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 } \
\text { Subject to: } & \mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } \geq 4 \
& \mathrm { X } _ { 1 } \geq 2 \
& \mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0
\end{array}$$
A)unique optimal solution
B)unbounded solution
C)infeasible solution
D)alternate optimal solution
E)redundant constraints

Quizplus · Accepted Answer

The feasible region is a closed and bounded triangular region. Since the objective function is a linear function, it takes its minimum value at a corner of the feasible region. The vertices of the feasible region are $(2, 2)$, $(4, 0)$, and $(0, 4)$. Plugging these points into the objective function, we get the values $10, 12,$ and $12$, respectively. Therefore the optimal solution is at $(2, 2)$ with the optimal objective function value of $10$. Since this is the only optimal solution, the answer is A.

Consider the Following Linear Programming Model This Linear Programming Model

Consider the Following Linear Programming Model
This Linear Programming Model