A tire manufacturer studying this effectiveness of television advertising on the sales of its GRIPPER-brand tires attempted to fit the data it had gathered into an equation

R(x) = a0 + a1x + a2x 2 ,   where S is sales revenue in millions of dollars,

x is millions of dollars spent on television advertising and a0, a1, a2 are constants.

The data was gathered in two different regions of the country. The resulting equations are

Region 1: R1(x) = 30 + 20x − 0.4x 2

Region 2: R2(x) = 20 + 36x − 1.3x 2

The company wants to know how to make the best use of its advertising dollars in the regions and whether current allocations could be improved. Your job is to advise management about current advertising effectiveness, allocation of additional expenditures, and reallocation of current expenditures by answering the following questions.

1) Which region would benefit more, if either, from additional advertising expenditures at each of the above levels of expenditures? Justify your answer USING MARGINAL RETURN ON SALES ANALYSIS.

2) Suppose money could be reallocated from Region 1 to Region 2 or vice-versa. At each of the above advertising allocation levels, explain what reallocation should be done, if any, to produce more sales revenue. [You don’t need an exact dollar amount, just what should be done and why. MAKE SURE THAT YOU JUSTIFY YOUR WORK IN TERMS OF MARGINAL RETURN ON SALES ANALYSIS.]