Variable Cells Constraints If the Coefficient of Activity 2 in the Objective Function

question 65

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 coefficient of Activity 2 in the objective function changes to $100, then:

• A) the original solution remains optimal.
• B) the problem must be resolved to find the optimal solution.
• C) the shadow price is valid.
• D) the shadow price is not valid.
• E) None of the choices is correct.

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Definitions:

Consumer Price Index

An index that measures the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.

Food and Beverage

This refers to the industry that encompasses the preparation, distribution, and service of food and drink products.

CPI

An index measuring the average change over time in the prices paid by urban consumers for a market basket of consumer goods and services.

Consumer Price Index

An index measuring the change over time in the price level of a market basket of consumer goods and services purchased by households.