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) \(f ( 8,4,12 ) = 212\)

Identify the effects of bidder valuation discrepancies on auction outcomes.

Understand the concept of bid shading and its strategic use in auctions.

Recognize the potential for collusion and its impact on auction outcomes.

Understand the basic concepts and types of auctions.

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