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:

Departments

Departments refer to distinct segments within an organization, each with specific responsibilities and roles, meant to streamline operations and improve efficiency.

Expenses

Costs incurred by a business in the process of earning revenue.

Indirect Costs

Costs that are not directly traceable to a specific product or service but are necessary for the operation of a business, such as overhead expenses.

Apportion

To divide and allocate proportions or shares of a total amount among different entities based on a set criteria or formula.