Bounds Inc. determined through regression analysis that its sales (S) are a function of the amount of advertising (measured in units) in two different media. This relationship is given by the...

Bounds Inc. determined through regression analysis that its sales (S) are a function of the amount of advertising (measured in units) in two different media. This relationship is given by the following equation (X = newspapers, Y = magazines):

S(X; Y) = 200X + 100Y - 10X²
- 20Y²
+ 20XY



a. Find the level of newspaper and magazine advertising that maximizes the firm’s sales.

b. Calculate the firm’s sales at the optimal values of newspaper and magazine advertising determined in part (a).