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Use the Following Management Scientist Output to Answer the Questions

question 30

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Use the following Management Scientist output to answer the questions.
MIN 4X1+5X2+6X3
S.T.
1)X1+X2+X3<85
2)3X1+4X2+2X3>280
3)2X1+4X2+4X3>320
Objective Function Value = 400.000  Variable  Value  Reduced Cost  X1 0.0001.500 X2 80.0000.000 X3 0.0001.000\begin{array} { c r c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { X1 } & 0.000 & 1.500 \\\text { X2 } & 80.000 & 0.000 \\\text { X3 } & 0.000 & 1.000\end{array}  Constraint  Slack/Surplus  Dual Price 15.0000.000240.0000.00030.0001.250\begin{array} { c 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} OBJECTIVE COEFFICIENT RANGES  Variable  Lower Limit  Current Value  Upper Limit  X1 2.5004.000 No Upper Limit  X2 0.0005.0006.000 X3 5.0006.000 No Upper Limit \begin{array} { c c c c } \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} RIGHT HAND SIDE RANGES  Constraint  Lower Limit  Current Value  Upper Limit 180.00085.000 No Upper Limit 2 No Lower Limit 280.000320.0003280.000320.000340.000\begin{array} { c c c c } \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:

Environmental Concerns

Issues related to the natural environment due to human activities or processes, including pollution, natural resource depletion, and climate change.

Strategic Planning

The process of defining a company's direction and making decisions on allocating resources to pursue this direction.

Competitive Intelligence

The gathering and analysis of information about competitors, market trends, and other external factors affecting a business's competitive position.

Globalization and Localization

The balance between adapting business practices to local cultures and markets (localization) while leveraging global trends and economies of scale (globalization).

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