Determine the Maximum Value of F(x, Y) = 4 - $x ^ { 2 }$

question 41

Short Answer

Determine the maximum value of f(x, y) = 4 - $x ^ { 2 }$ - $y ^ { 2 }$ subject to the constraint $y = 3 x - 4$ .
Enter your answer as exactly just a, b where a is the maximum and b is the Lagrange multiplier as either integers or reduced fractions of form $\frac { \mathrm { c } } { \mathrm { d } }$ (no words or labels).

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Definitions:

Supply Curve

A graphical representation showing the relationship between the price of a good and the quantity supplied by producers.

Complement

A good or service that is used together with another, increasing demand for both as the use of one enhances the value or utility of the other.

Demand Curve

A graph plotting the quantity of a good that buyers wish to purchase at different price levels, typically sloping downwards from left to right.

Consumer Confidence

A measure of the overall consumer optimism about the state of an economy, reflected through spending and saving behaviors.