Consider the Following Linear Program The Management Scientist Provided the Following Solution Output:
OPTIMAL SOLUTION

question 50

Essay

Consider the following linear program:
$$\begin{array} { c r } \text { Min } & 6 x _ { 1 } + 9 x _ { 2 } ( \$ \text { cost } ) \\\text { s.t. } & x _ { 1 } + 2 x _ { 2 } \leq 8 \\& 10 x _ { 1 } + 7.5 x _ { 2 } \geq 30 \\&x _ { 2 } \geq 2 \\&x _ { 1 } , x _ { 2 } \geq 0\end{array}$$
The Management Scientist provided the following solution output:
OPTIMAL SOLUTION
Objective Function Value = 27.000 $$\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Cost } \\\text { X1 } & 1.500 & 0.000 \\\text { X2 } & 2.000 & 0.000\end{array}$$ $$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Price } \\1 & 2.500 & 0.000 \\2 & 0.000 & - 0.600 \\3 & 0.000 & - 4.500\end{array}$$ OBJECTIVE COEFFICIENT RANGES $$\begin{array} { c c c c } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\text { X1 } & 0.000 & 6.000 & 12.000 \\\text { X2 } & 4.500 & 9.000 & \text { No Upper Limit }\end{array}$$ RIGHT HAND SIDE RANGES $$\begin{array} { c c c c } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\1 & 5.500 & 8.000 & \text { No Upper Limit } \\2 & 15.000 & 30.000 & 55.000 \\3 & 0.000 & 2.000 & 4.000\end{array}$$
a.What is the optimal solution including the optimal value of the objective function?
b.Suppose the unit cost of x₁ is decreased to $4. Is the above solution still optimal? What is the value of the objective function when this unit cost is decreased to $4?
c.How much can the unit cost of x₂ be decreased without concern for the optimal solution changing?
d.If simultaneously the cost of x₁ was raised to $7.5 and the cost of x₂ was reduced to $6, would the current solution still remain optimal?
e.If the right-hand side of constraint 3 is increased by 1, what will be the effect on the optimal solution?

Recognize the effects of stress and environment on infant brain development.

Identify the dimensions of temperament in infancy and their impact on behavior.

Define self-awareness in infants and its developmental milestones.

Explain the role of meaningful connections between brain regions in emotional regulation.

---

Definitions:

Two Years

A period equivalent to 24 months, a significant timeframe in early development marked by rapid changes in motor, cognitive, and social skills.

Terminally Ill Person

An individual diagnosed with a disease that is incurable and expected to lead to death.

Americans

People who are citizens of or living in the United States.

Kept Alive

Maintained in a state of being alive or functioning, especially under conditions where cessation is a possibility.