Use Lagrange Multipliers to Find the Maximum Value of the Function

question 26

Multiple Choice

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.
$$f ( x , y , z ) = 14 x + 8 y + 12 z , x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 101$$

• A) \(f ( 14,8,12 ) = 404\)
• B) \(f ( 20,9,18 ) = 568\)
• C) \(f ( 7,4,6 ) = 202\)
• D) \(f ( 18,17,5 ) = 308\)
• E) \(f ( 8,4,12 ) = 212\)

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Definitions:

Linea Alba

A fibrous structure that runs down the midline of the abdomen, forming part of the abdominal wall and separating the left and right abdominal muscles.

Symphysis Pubis

A cartilaginous joint located between the left and right pubic bones at the front of the pelvis, providing slight mobility and acting as a shock absorber.

Pubic Crest

The ridge at the top of the pubic bone, serving as an attachment point for abdominal muscles.

Rectus Abdominis

The rectus abdominis is a long muscle that extends along the front of the abdomen, playing a key role in maintaining posture and facilitating movement.