I. Marginal Return to Sales
A tire manufacturer studying the effectiveness of television advertising and other promotions on sales of its GRIPPER-brand tires attempted to fit data it had gathered to the equation
where S is sales revenue in millions of dollars, x is millions of dollars spent on television advertising, y is millions of dollars spent on other promotions, and , and are constants. The data, gathered in two different regions of the country where expenditures for other promotions were kept constant (at and ), resulted in the following quadratic equations relating TV advertising and sales.
The company wants to know how to make the best use of its advertising dollars in the regions and whether the current allocation could be improved. Advise management about current advertising effectiveness, allocation of additional expenditures, and reallocation of current advertising expenditures by answering the following questions.
If any additional money is made available for advertising, in which region should it be spent?
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