The Linear Programming Problem Whose Output Follows Determines How Many

question 25

Short Answer

The linear programming problem whose output follows determines how many red nail polishes, blue nail polishes, green nail polishes, and pink nail polishes a beauty salon should stock. The objective function measures profit; it is assumed that every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Constraints 3 and 4 are marketing restrictions.
MAX    100x1 + 120x2 + 150x3 + 125x4
Subject to    1. x1 + 2x2 + 2x3 + 2x4 ? 108
      2. 3x1 + 5x2 + x4 ? 120
      3. x1 + x3 ? 25
      4. x2 + x3 + x4 > 50
      x1, x2, x3, x4 ? 0
Optimal Solution:
Objective Function Value = 7475.000
$$\begin{array} { c c c } \text { Variable } & \text { Value } & \text { Reduced Costs } \\\hline \text { X1 } & 8 & 0 \\\text { X2 } & 0 & 5 \\\text { X3 } & 17 & 0 \\\text { X4 } & 33 & 0 \\\hline\end{array}$$
$$\begin{array} { c c c } \text { Constraint } & \text { Slack/Surplus } & \text { Dual Prices } \\\hline 1 & 0 & 75 \\2 & 63 & 0 \\3 & 0 & 25 \\4 & 0 & - 25 \\\hline\end{array}$$ Objective Coefficient Ranges
$$\begin{array} { c c c c } \text { Variable } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\hline \text { X1 } & 87.5 & 100 & \text { none } \\\text { X2 } & \text { none } & 120 & 125 \\\text { X3 } & 125 & 150 & 162 \\\text { X4 } & 120 & 125 & 150\end{array}$$ Right Hand Side Ranges
$$\begin{array} { c c c c } \text { Constraint } & \text { Lower Limit } & \text { Current Value } & \text { Upper Limit } \\\hline 1 & 100 & 108 & 123.75 \\2 & 57 & 120 & \text { none } \\3 & 8 & 25 & 58 \\4 & 41.5 & 50 & 54 \\\hline\end{array}$$
-How much space will be left unused?

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Definitions:

Assimilation

The process of taking in new information into our previously existing schemas.

Accommodation

A cognitive process in Piaget's theory, where existing mental schemas are modified or new ones created in response to new information.

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A systematic approach in the medical field for diagnosing, treating, and observing patients.

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Pertaining to the Socratic method, an approach to teaching that uses question-and-answer dialogue to stimulate critical thinking and illuminate ideas.