The Function $z = x y + ( x + y ) ( 120 - x - y )$

question 80

Essay

The function $z = x y + ( x + y ) ( 120 - x - y )$ has a maximum. Find the values of $x$ and $y$ at which it occurs.

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Definitions:

Scatter Diagram

A graphical representation of data points on a Cartesian coordinate system, used to observe the relationship between two variables.

Estimated Regression Equation

An equation derived from regression analysis that estimates the relationship between variables.

Independent Variable

A variable presumed to influence or determine the dependent variable in an experiment or study.

Coefficient of Determination

A statistical measure that determines the proportion of variance in the dependent variable that can be predicted from the independent variable(s).