Use Lagrange Multipliers to Find the Maximum Value of the Function

question 39

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

Understand the impact of market demand on equilibrium price in a purely competitive market.

Compare short-run and long-run decision-making in purely competitive firms.

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Recognize the physiological benefits of aerobic fitness, including its impact on mortality and cardiovascular health.

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Definitions:

Capacitation

Maturation process that enables mammalian sperm to participate in fertilization; takes place in the female reproductive tract.

Acrosome Reaction

A series of events in which the acrosome, a caplike structure covering the head of a sperm cell, releases proteolytic (protein-digesting) enzymes and undergoes other changes that permit the sperm to penetrate the outer covering of the egg.

Spermatogenesis

The process by which sperm cells are produced in male gonads, involving both mitosis and meiosis, resulting in haploid sperm from diploid cells.

Blastomere

A type of cell produced by the division of the egg after fertilization, contributing to the formation of the embryo.