Use the Following Management Scientist Output to Answer the Questions

question 41

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 $$\begin{array} { c r c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { X1 } & 0.000 & 1.500 \\\text { X2 } & 80.000 & 0.000 \\\text { X3 } & 0.000 & 1.000\end{array}$$ $\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Frice } \\ 1 & 5.000 & 0.000 \\ 2 & 40.000 & 0.000 \\ 3 & 0.000 & - 1.250 \end{array}$
OBJECTIVE COEFFICIENT RANGES
$\begin{array}{lllc}\text { Variable }&\text { Lower Limit } & \text { Current Value } & \text { Upper Limit }\\\hline\mathrm{X} 1 & 2.500 & 4.000 & \text { No Upper Limit } \\\mathrm{X} 2 & 0.000 & 5.000 & 6.000 \\\mathrm{X} 3 & 5.000 & 6.000 & \text { No Upper Limit }\end{array}$
$\text { RIGHT HAND SIDE RANGES }$
$\begin{array}{cccc}\text { Constraint }&\text { Lower Limit } & \text { Current Value } & \text { Upper Limit }\\\hline1 & 80.000 & 85.000 & \text { No Upper Limit } \\2 & \text { No Lower Limit } & 280.000 & 320.000 \\3 & 280.000 & 320.000 & 340.000\end{array}$
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:

Official Statistics

Data collected and published by government agencies or other official organizations.

Median

The middle value in a data set, where half the numbers are lower and half are higher.

Mean

In mathematics, the average or central value of a set of numbers, calculated by dividing the sum of the values in the set by the number of values.

Correlation Coefficient

A statistical measure that indicates the extent to which two variables change together, showing the strength and direction of their relationship.