Which of the Constraints Are Binding at the Optimal Solution

question 50

Essay

Which of the constraints are binding at the optimal solution for the following problem and Risk Solver Platform (RSP) sensitivity output?
$$\begin{array} { l l } \operatorname { MAX } : & 7 \mathbf { X } _ { 1 } + 4 \mathbf { X } _ { \mathbf { 2 } } \\\text { Subject ta: } & 2 \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } \leq 10 \\& \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } \leq 10 \\& 2 \mathbf { X } _ { 1 } + 5 \mathbf { X } _ { \mathbf { 2 } } \leq 40 \\& \mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \geq \mathbf {0 }\end{array}$$ $\text {Changing Calls}$
$\begin{array}{llrrrrr}&&\text { Final} &\text {Reduced }&\text {Objective }&\text {Allowable}&\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{~B} \$ 4 & \text { Number to make: } \mathrm{X} 1 &6& 0 & 7& 1& 3 \\\$ \mathrm{C} \$ 4 & \text { Number to make: } \mathrm{X} 2 & 4 & 0 & 4 &3 & 0.5\end{array}$

$\text {Constraints}$
$\begin{array}{llrrrrr}&&\text { Final } &\text {Shadow} &\text { Constraint } &\text {Allowable} &\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Price } & \text { R.H. Side } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{D} \$ 8 & \text { Used } & 16& 3 & 16 & 4 &2.67 \\\$ \mathrm{D} \$ 9 & \text { Used } & 10 & 1 & 10 & 1 & 2 \\\$ \mathrm{D} \$ 10 & \text { Used } & 32& 0 & 40 & 1 E+30 & 8\end{array}$

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