A tire manufacturer studying the effectiveness of television advertising and other promotions on sales of its...

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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 = ao + a1x + a2x2 + b1y 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 ao, a,, a2, and b, are constants. The data, gathered in two different regions of the country where expenditures for other promotions are kept constant (at B1 and B2), resulted in the following quadratic equations relations TV advertising and sales. = 34 + 17x - 0.5x2 + B1 Region 1: S1 Region 2: S2 = 16 + 37x – 1.3x2 + B2 The company wants to know how to make the best use of its advertising dollars in the regions and whether the current allocation of $10 million for each region could be improved. Advise management about current advertising effectiveness, allocation of additional expenditures, and reallocation of current advertising expenditures by answering the following questions. 1. In the analysis of sales and advertising, marginal return to sales is usually used, and it is given ds by dx' a. Find the marginal return to sales for each region. b. If $10 million is being spent on TV advertising in each region, what is the marginal return to sales in each region? 2. Which region would benefit more from additional advertising expenditure, if $10 million is currently being spent in each region? 3. If any amount of additional money is made available for advertising, in which region should it be spent? 4. How could money already being spent be reallocated to produce more sales revenue? 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 = ao + a1x + a2x2 + b1y 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 ao, a,, a2, and b, are constants. The data, gathered in two different regions of the country where expenditures for other promotions are kept constant (at B1 and B2), resulted in the following quadratic equations relations TV advertising and sales. = 34 + 17x - 0.5x2 + B1 Region 1: S1 Region 2: S2 = 16 + 37x – 1.3x2 + B2 The company wants to know how to make the best use of its advertising dollars in the regions and whether the current allocation of $10 million for each region could be improved. Advise management about current advertising effectiveness, allocation of additional expenditures, and reallocation of current advertising expenditures by answering the following questions. 1. In the analysis of sales and advertising, marginal return to sales is usually used, and it is given ds by dx' a. Find the marginal return to sales for each region. b. If $10 million is being spent on TV advertising in each region, what is the marginal return to sales in each region? 2. Which region would benefit more from additional advertising expenditure, if $10 million is currently being spent in each region? 3. If any amount of additional money is made available for advertising, in which region should it be spent? 4. How could money already being spent be reallocated to produce more sales revenue?