Use Lagrange Multipliers to Find the Maximum Value of F $f \left( \frac { 3 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 243 } { 16 }$

question 6

Multiple Choice

Use Lagrange multipliers to find the maximum value of f (x,y) = 9xy subject to the constraint 9x + 3y = 27.

• A)f (0,0)= 0
• B)f (3,9)= 243
• C) \(f \left( \frac { 3 } { 4 } , \frac { 9 } { 4 } \right) = \frac { 243 } { 16 }\)
• D) \(f \left( \frac { 3 } { 2 } , \frac { 9 } { 2 } \right) = \frac { 243 } { 4 }\)

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Definitions:

Differentiated Oligopoly

An oligopoly in which firms produce a differentiated product.

Negative-Sum Games

Situations or games where the total losses exceed the total gains, meaning the net outcome is negative for the involved parties.

Mutual Interdependence

Mutual interdependence occurs in markets where the actions of one firm significantly impact the operations, outcomes, or decisions of other firms within the same market.

Monopolistic Competition

A market structure in which many companies sell products that are similar but not identical, allowing for significant differentiation and some control over pricing.