Let $L ( x , y ) = a x + b y$

question 32

Essay

Let $L ( x , y ) = a x + b y$ .Find values of a and b so that $L ( x , y )$ takes a maximum value of 4 on the unit circle $x ^ { 2 } + y ^ { 2 } = 1$ at the point $\left( \frac { 1 } { 2 } , \frac { - \sqrt { 3 } } { 2 } \right)$ .

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Definitions:

GATT

The General Agreement on Tariffs and Trade, a multilateral treaty aimed at reducing trade barriers and promoting international trade through the reduction of tariffs and quotas.

World Trade Organization

An international organization designed to regulate and facilitate international trade between nations.

General Agreement on Tariffs and Trade

An international treaty that aimed to reduce tariffs and other trade barriers, leading to the establishment of the World Trade Organization.

Import Quotas

Restrictions set by the government on the amount or monetary worth of products allowed into a nation, aimed at shielding local businesses from overseas rivals.