A Closed Rectangular Box with Square Ends Is to Be $x ^ { 2 }$

question 118

Multiple Choice

A closed rectangular box with square ends is to be designed so that the surface area of the box is minimized. [Note: Surface area = 2 $x ^ { 2 }$ + 4xy.] It is required that the volume be 32 cubic inches. Which of the following is the Lagrange function F(x, y, λ) for this problem?

• A) 2 \(x ^ { 2 }\) + 4xy + λ(32)
• B) ( \(x ^ { 2 }\) y - 32) + λ(2 \(x ^ { 2 }\) + 4xy)
• C) 2 \(x ^ { 2 }\) + 4xy + λ( \(x ^ { 2 }\) y - 32)
• D) \(x ^ { 2 }\) y + λ(2 \(x ^ { 2 }\) + 4xy - 32)
• E) none of these

Understand the complex etiology of schizophrenia, including genetic, neurological, and environmental factors.

Recognize the significance of the diathesis-stress model in understanding the development of schizophrenia and the interaction of vulnerability and stress factors.

Analyze the reliability and validity of symptom-based subtypes of schizophrenia and the challenges in categorization.

Evaluate the evidence surrounding biological aspects of schizophrenia, including the role of dopamine, brain structure abnormalities, and prenatal risks.