Use the Following Management Scientist Output to Answer the Questions $\mathrm { X } 1 + \mathrm { X } 2 + \mathrm { X } 3 < 85$

question 23

Essay

Use the following Management Scientist output to answer the questions.
MIN 4X1+5X2+6X3
S.T.
Objective Function Value = 400.000
1) $\mathrm { X } 1 + \mathrm { X } 2 + \mathrm { X } 3 < 85$
2) $3 \mathrm { X } 1 + 4 \mathrm { X } 2 + 2 \mathrm { X } 3 > 280$
3) $2 X 1 + 4 X 2 + 4 X 3 > 320$ $$\begin{array} { l c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\mathrm { X } 1 & 0.000 & 1.500 \\\mathrm { X } 2 & 80.000 & 0.000 \\\mathrm { X } 3 & 0.000 & 1.000\end{array}$$ OBJECTIVE COEFFICIENT RANGES
$$\begin{array} { l c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 5.000 & 0.000 \\2 & 40.000 & 0.000 \\3 & 0.000 & - 1.250\end{array}$$ RIGHT HAND SIDE RANGES
$$\begin{array} { l l l l } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\text { X1 } & 2.500 & 4.000 & \text { No Upper Limit } \\\text { X2 } & 0.000 & 5.000 & 6.000 \\\text { X3 } & 5.000 & 6.000 & \text { No Upper Limit }\end{array}$$ $$\begin{array} { l l c l } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\1 & 80.000 & 85.000 & \text { No Upper Limit } \\2 & \text { No Lower Limit } & 280.000 & 320.000 \\3 & 280.000 & 320.000 & 340.000\end{array}$$
a.What is the optimal solution,and what is the value of the profit contribution?
b.Which constraints are binding?
c.What are the dual prices for each resource? Interpret.
d.Compute and interpret the ranges of optimality.
e.Compute and interpret the ranges of feasibility.

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Definitions:

Trigger Points

Specific conditions, thresholds, or events that activate or initiate a particular action or response.

Different Conditions

Refers to varied circumstances or environments in which a task, process, or experiment is carried out, impacting outcomes or results.

Quantitative Forecasting

The use of statistical models and historical data to predict future trends or outcomes.

Correlation

A statistical measure that indicates the extent to which two or more variables fluctuate together.