A Rancher Plans to Use an Existing Stone Wall and the Side

question 16

Multiple Choice

A rancher plans to use an existing stone wall and the side of a barn as a boundary for two adjacent rectangular corrals. Fencing for the perimeter costs 15 per foot. To separate the corrals, a fence that costs 6 per foot will divide the region. The total area of the two corrals is to be $6000$ square feet. Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing.

• A)dimensions: \(50\) feet by \(60\) feet
• B)dimensions: \(60\) feet by \(50\) feet
• C)dimensions: \(25\) feet by \(60\) feet
• D)dimensions: \(30\) feet by \(50\) feet
• E)dimensions: \(25\) feet by \(30\) feet

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Definitions:

Perspective-taking Skills

The cognitive capacity to view situations from the viewpoints of others, facilitating empathy and social understanding.

More Than One Perspective

The recognition that there can be multiple viewpoints or interpretations of a given situation, reflecting the complexity of human thought and understanding.

Robert Selman

A psychologist known for his work in the development of social understanding in children and his stages of perspective-taking.

Social Cognitive Theory

A theoretical framework that outlines how people learn by observing others, incorporating concepts of observed behaviors, imitations, and modeling.