Case Study Read the case situation below and answer
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=ap + ax + a2x² + by
where s is sales revenue in millions of dollars, x is millions of dollars on television advertising, y is million of dollars spent on other promotions, and as a, a, and by are constants. The data, gathered in two different regions of the country were expenditures for other promotions were kept constant (at B₁ and B₂), resulted in the following quadratic equations relating TV advertising and sales.
- Region 2: S₂ = 20 + 36x - 1.3x2 + B₂ Region 1: S₁=30+20x −0.4x² + B₁ 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.
1. In the analysis of sales and advertising, marginal return to sales is usually used, and it is given by dS₁/dx for Region 1 and dS₂/dx for region 2.
(a) Find and dx
(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 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?
