Use the Following Management Scientist Output to Answer the Questions $3 X 1 + 5 X 2 + 2 X 3 > 90$

question 2

Essay

Use the following Management Scientist output to answer the questions.
LINEAR PROGRAMMING PROBLEM
MAX 31X1+35X2+32X3
S.T.
OPTIMAL SOLUTION
Objective Function Value = 763.333
1) $3 X 1 + 5 X 2 + 2 X 3 > 90$
2) $6 \mathrm { X } 1 + 7 \mathrm { X } 2 + 8 \mathrm { X } 3 < 150$
3) $5 \mathrm { X } 1 + 3 \mathrm { X } 2 + 3 \mathrm { X } 3 < 120$ $$\begin{array} { l c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\mathrm { X } 1 & 13.333 & 0.000 \\\mathrm { X } 2 & 10.000 & 0.000 \\\mathrm { X } 3 & 0.000 & 10.889\end{array}$$ OBJECTIVE COEFFICIENT RANGES
$$\begin{array} { l c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & - 0.778 \\2 & 0.000 & 5.556 \\3 & 23.333 & 0.000\end{array}$$ RIGHT HAND SIDE RANGES
$$\begin{array} { l l l l } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\text { X1 } & 30.000 & 31.000 & \text { No Upper Limit } \\\text { X2 } & \text { No Lower Limit } & 35.000 & 36.167 \\\text { X3 } & \text { No Lower Limit } & 32.000 & 42.889\end{array}$$ $$\begin{array} { l c c l } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\1 & 77.647 & 90.000 & 107.143 \\2 & 126.000 & 150.000 & 163.125 \\3 & 96.667 & 120.000 & \text { No Upper Limit }\end{array}$$
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:

Lateral Hemisphere

Refers to either the left or right half of the cerebrum in the brain, responsible for controlling different functions and processes.

Pontine Nuclei

Clusters of neurons in the pons part of the brainstem that play a crucial role in motor control and sensory analysis.

Respiration

The biochemical process by which living organisms exchange gases with their environment, involving the intake of oxygen and release of carbon dioxide.

Blood Pressure

The force exerted by circulating blood on the walls of blood vessels, critical for ensuring that blood flows throughout the body.