Consider the Following Linear Program:
the Management Scientist Provided the Following

question 52

Essay

Consider the following linear program:
The Management Scientist provided the following solution output:
OPTIMAL SOLUTION
Objective Function Value = 20.000
MIAX $3 x _ { 1 } + 4 x 2 ( \$$ Profit $)$
s.t.
$x _ { 1 } + 3 x _ { 2 } \leq 12$
$2 x _ { 1 } + x _ { 2 } \leq 8$
$x 1 \leq 3$
$x _ { 1 } , x _ { 2 } \geq 0$ $$\begin{array} { l l l } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\mathrm { X } 1 & 2.400 & 0.000 \\\mathrm { X } 2 & 3.200 & 0.000\end{array}$$ OBJECTIVE COEFFICIENT RANGES
$$\begin{array} { l l l } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 0.000 & 1.000 \\2 & 0.000 & 1.000 \\3 & 0.600 & 0.000\end{array}$$ RIGHT HAND SIDE RANGES
$$\begin{array} { l l l l } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\text { X1 } & 1.333 & 3.000 & 8.000 \\\mathrm { X } 2 & 1.500 & 4.000 & 9.000\end{array}$$ $$\begin{array} { l l c c } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\1 & 9.000 & 12.000 & 24.000 \\2 & 4.000 & 8.000 & 9.000 \\3 & 2.400 & 3.000 & \text { No Upper Limit }\end{array}$$
a.What is the optimal solution including the optimal value of the objective function?
b.Suppose the profit on x₁ is increased to $7.Is the above solution still optimal? What is the value of the objective function when this unit profit is increased to $7?
c.If the unit profit on x₂ was $10 instead of $4,would the optimal solution change?
d.If simultaneously the profit on x₁ was raised to $5.5 and the profit on x₂ was reduced to $3,would the current solution still remain optimal?

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Definitions:

Inhibitory Synapse

A type of synaptic connection that decreases the likelihood of the receiving neuron firing an action potential.

Excitatory Synapse

A synapse at which an action in the presynaptic neuron increases the probability of an action potential occurring in the postsynaptic cell, typically by releasing neurotransmitters.

Object Recognition

The cognitive process of identifying and recognizing objects through visual perception.

Temporal Lobes

The regions of the cerebral cortex located on the sides of the brain, involved in processing sensory input and are important for memory, speech, and recognizing faces.