Consider the Following Linear Programming Model and Risk Solver Platform

question 64

Essay

Consider the following linear programming model and Risk Solver Platform (RSP) sensitivity output. What is the optimal objective function value if the RHS of the first constraint increases to 18?
$$\begin{array} { l l } \operatorname { MAX } : & 7 \mathbf { X } _ { 1 } + 4 \mathbf { X } _ { \mathbf { 2 } } \\\text { Subject ta: } & 2 \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } \leq 10 \\& \mathbf { X } _ { 1 } + \mathbf { X } _ { \mathbf { 2 } } \leq 10 \\& 2 \mathbf { X } _ { 1 } + 5 \mathbf { X } _ { \mathbf { 2 } } \leq 40 \\& \mathbf { X } _ { 1 } \mathbf { X } _ { \mathbf { 2 } } \geq \mathbf { 0 }\\\end{array}$$ $\text {Changing Calls}$
$\begin{array}{llrrrrr}&&\text { Final} &\text {Reduced }&\text {Objective }&\text {Allowable}&\text { Allowable }\\\text { Cell } & \text { Name } & \text { Value } & \text { Cost } & \text { Coefficient } & \text { Increase } & \text { Decrease } \\\hline \$ \mathrm{~B} \$ 4 & \text { Number to make: } \mathrm{X} 1 &6& 0 & 7& 1& 3\\\$ \mathrm{C} \$ 4 & \text { Number to make: } \mathrm{X} 2 & 4 & 0 &4 &3 & 0.5\\\end{array}$

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

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