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Is the Optimal Solution to This Problem Unique, or Is MAX5X1+2X2\mathrm { MAX } \quad 5 \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 }

Question 41

Essay

Is the optimal solution to this problem unique, or is there an alternate optimal solution? Explain your reasoning.
MAX5X1+2X2\mathrm { MAX } \quad 5 \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 }
Subject ta:
3X1+5X21510X1+4X220X1,X20\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} Changing Calls\text {Changing Calls}
 FinalReduced Objective Allowable Allowable  Cell  Name  Value  Cost  Coefficient  Increase  Decrease $ B$4 Number to make: X12051E+300$C$4 Number to make: X200201E+30\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}

Constraints\text {Constraints}
 Final Shadow Constraint Allowable Allowable  Cell  Name  Value  Price  R.H. Side  Increase  Decrease $D$8 Used 60151E+309$D$9 Used 200.5203020\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}

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