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:

Compounded Rate

The rate at which interest is calculated on the initial principal and the accumulated interest of previous periods.

Compounded Monthly

The calculation of interest on both the initial principal and the accumulated interest from previous months.

Monthly Payments

Payments that are due every month, as in the case of a loan or lease.

Withdrawals

Acts of removing funds from a savings or investment account, which can impact the account's growth or income-producing ability.