Use the Following Management Scientist Output to Answer the Questions

question 12

Essay

Use the following Management Scientist output to answer the questions.
LINEAR PROGRAMMING PROBLEM
MAX
31X1+35X2+32X3
S.T.
1) 3X1+5X2+2X3>90
2) 6X1+7X2+8X3<150
3) 5X1+3X2+3X3<120
OPTIMAL SOLUTION
Objective Function Value = 763.333 $$\begin{array} { c r c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { X1 } & 13.333 & 0.000 \\\text { X2 } & 10.000 & 0.000 \\\text { X3 } & 0.000 & 10.889\end{array}$$ $\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\ 1 & 0.000 & - 0.778 \\ 2 & 0.000 & 5.556 \\ 3 & 23.333 & 0.000 \end{array}$
OBJECTIVE COEFFICIENT RANGES
$\begin{array}{cccc}\text { Variable }&\text { Lower Limit } & \text { Current Value } & \text { Upper Limit }\\\hline\text { X1 } & 30.000 & 31.000 & \text { No Upper Limit } \\\text { X2 } & \text { No Lower Limit } & 35.000 & 36.167 \\\text { X3 } & \text { No Lower Limit } & 32.000 & 42.889\end{array}$
$\text { RIGHT HAND SIDE RANGES }$
$\begin{array}{cccc}\text { Constraint }&\text { Lower Limit } & \text { Current Value } & \text { Upper Limit }\\\hline1 & 77.647 & 90.000 & 107.143 \\2 & 126.000 & 150.000 & 163.125 \\3 & 96.667 & 120.000 & \text { No Upper Limit }\end{array}$
a.Give the solution to the problem.
b.Which constraints are binding?
c.What would happen if the coefficient of x₁ increased by 3?
d.What would happen if the right-hand side of constraint 1 increased by 10?

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Definitions:

Modes of Interacting

Different ways or methods through which individuals communicate or engage with each other.

Communicate

The process of conveying information or expressing ideas and feelings through verbal, nonverbal, or written means.

Opinions

Personal beliefs or judgments that are not founded on proof or certainty, reflecting individual perspectives or preferences.

Personal Unhappiness

A state of dissatisfaction or sadness with one's personal situation or life circumstances.