Use the Following Management Scientist Output to Answer the Questions

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.