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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 S = a 0 + a 1 x + a 2 x 2 + b 1 y 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 a 0 , a 1 , a 2 , and b 1 are constants. The data, gathered in two different regions of the country where expenditures for other promotions were kept constant (at B 1 and B 2 ), resulted in the following quadratic equations relating TV advertising and sales. Region 1: S 1 = 30 + 20 x − 0.4 x 2 + B 1 Region m: S 2 = 20 + 36 x − 1.3 x 2 + B 2 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. Which region would benefit more from additional advertising expenditure, if $10 million is currently being spent in each region?

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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781305108042
Chapter 9, Problem 2EAGP1
Textbook Problem
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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

S = a 0 + a 1 x + a 2 x 2 + b 1 y

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 a 0 , a 1 , a 2 , and b 1 are constants. The data, gathered in two different regions of the country where expenditures for other promotions were kept constant (at B 1 and B 2 ), resulted in the following quadratic equations relating TV advertising and sales.

Region 1: S 1 = 30 + 20 x 0.4 x 2 + B 1

Region m: S 2 = 20 + 36 x 1.3 x 2 + B 2

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.

Which region would benefit more from additional advertising expenditure, if $10 million is currently being spent in each region?

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