Variable Cells Constraints If the Right-Hand Side of Resource C Is Increased by Name

question 66

Multiple Choice

Variable cells
$\begin{array}{|r|r|r|r|r|r|r|}\hline \text { Cell } & \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Reduced } \\\text { Cost }\end{array} & \begin{array}{c}\text { Objective } \\\text { Coefficient }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \$ \mathrm{B} \$ 6 & \text { Activity 1 } & 0 & 425 & 500 & 1 \mathrm{E}+30 & 425 \\\hline \$ \mathrm{C} \$ 6 & \text { Activity 2 } & 27.5 & 0.0 & 300 & 500 & 300 \\\hline \$ \mathrm{D} \$ & \text { Activity 3 } & 0 & 250 & 400 & 1 \mathrm{E}+30 & 250 \\\hline\end{array}$
Constraints
$\begin{array}{|r|r|r|r|r|r|r|}\hline \text { Cell } & \text { Name } & \begin{array}{c}\text { Final } \\\text { Value }\end{array} & \begin{array}{c}\text { Shadow } \\\text { Price }\end{array} & \begin{array}{c}\text { Constraint } \\\text { R.H. Side }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Increase }\end{array} & \begin{array}{c}\text { Allowable } \\\text { Decrease }\end{array} \\\hline \$ \mathrm{E} \$ 2 & \text { Benefit A } & 110 & 0 & 60 & 50 & 1 \mathrm{E}+3 \mathrm{C} \\\hline \$ \mathrm{E} \$ 3 & \text { Benefit B } & 110 & 75 & 110 & 1 \mathrm{E}+30 & 46 \\\hline \$\mathrm{E} \$ 4 & \text { Benefit C } & 137.5 & 0 & 80 & 57.5 & 1 \mathrm{E}+30 \\\hline\end{array}$
If the right-hand side of Resource C is increased by 40, and the right-hand side of Resource B is decreased by 20, then:

• A) the optimal solution remains the same.
• B) the optimal solution will change.
• C) the shadow price is valid.
• D) the shadow price may or may not be not valid.
• E) None of the choices is correct.

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Definitions:

Regio-

A prefix used in chemistry to describe directionality or specific regions in molecules, particularly important in reactions with more than one possible outcome.

Major Organic

Refers to the primary organic (carbon-containing) compound or product resulting from a chemical reaction.

Alkene

A hydrocarbon containing at least one carbon-carbon double bond, part of the unsaturated hydrocarbon family.

Compound

A substance formed when two or more chemical elements are chemically bonded together.