Use the Following Management Scientist Output to Answer the Questions

question 30

Essay

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 $$\begin{array} { c r c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { X1 } & 0.000 & 1.500 \\\text { X2 } & 80.000 & 0.000 \\\text { X3 } & 0.000 & 1.000\end{array}$$ $$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 5.000 & 0.000 \\2 & 40.000 & 0.000 \\3 & 0.000 & - 1.250\end{array}$$ OBJECTIVE COEFFICIENT RANGES $$\begin{array} { c c c c } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\text { X1 } & 2.500 & 4.000 & \text { No Upper Limit } \\\text { X2 } & 0.000 & 5.000 & 6.000 \\\text { X3 } & 5.000 & 6.000 & \text { No Upper Limit }\end{array}$$ RIGHT HAND SIDE RANGES $$\begin{array} { c c c c } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\1 & 80.000 & 85.000 & \text { No Upper Limit } \\2 & \text { No Lower Limit } & 280.000 & 320.000 \\3 & 280.000 & 320.000 & 340.000\end{array}$$
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:

Department Manager

A professional responsible for overseeing the operations, staff, and budget of a department within an organization.

Investment Center

A decentralized unit in which the manager has the responsibility and authority to make decisions that affect not only costs and revenues but also the fixed assets available to the center.

Authority

The power or right to make decisions, direct others, and enforce obedience within a particular scope.

Plant Assets

Fixed assets that are tangible in nature, such as buildings and machinery, used in the operations of a business and expected to be useful for many years.