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:

Participative Behaviours

Actions that involve employees in decision-making processes and grant them a degree of influence over their work and work environment.

Research Evidence

Information or data that supports a theory, hypothesis, or claim, often gathered through scientific methods.

Task Leadership

Leadership focused on accomplishing specific objectives by directing and organizing work activities.

Supportive Leadership

A leadership style characterized by attention to employees' needs, showing empathy, and providing encouragement and support.