Is the Optimal Solution to This Problem Unique, or Is $\mathrm { MAX } \quad 5 \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 }$

Essay

Is the optimal solution to this problem unique, or is there an alternate optimal solution? Explain your reasoning.
$\mathrm { MAX } \quad 5 \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 }$
Subject ta:
$\begin{array} { l } 3 X _ { 1 } + 5 X _ { \mathbf { 2} } \leq 15 \\10 X _ { 1 } + 4 X _ { \mathbf { 2 } } \leq 20 \\X _ { 1 } , X _ { 2 } \geq 0\end{array}$ $\text {Changing Calls}$
$\begin{array}{llrrrrr}&&\text { Final} &\text {Reduced }&\text {Objective }&\text {Allowable}&\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{~B} \$ 4 & \text { Number to make: } \mathrm{X} 1 &2& 0 & 5& 1E+30& 0 \\\$ \mathrm{C} \$ 4 & \text { Number to make: } \mathrm{X} 2 & 0 & 0 & 2 &0 & 1E+30\end{array}$

$\text {Constraints}$
$\begin{array}{llrrrrr}&&\text { Final } &\text {Shadow} &\text { Constraint } &\text {Allowable} &\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{D} \$ 8 & \text { Used } & 6&0 & 15 & 1E+30 &9 \\\$ \mathrm{D} \$ 9 & \text { Used } & 20 & 0.5 & 20 & 30 & 20 \\\end{array}$