The manufacturer of GRIPPER tires modeled its return to sales from television advertising expenditures in two regions, as follows: Region1: Region2: where and are the sales revenue in millions of dollars, and and are millions of dollars of expenditures for television advertising. How much money will be needed to maximize sales revenue in both districts? Round your answer to the nearest million dollars.

Question

The manufacturer of GRIPPER tires modeled its return to sales from television advertising expenditures in two regions, as follows: Region1:  Region2:  where  and  are the sales revenue in millions of dollars, and  and  are millions of dollars of expenditures for television advertising. How much money will be needed to maximize sales revenue in both districts? Round your answer to the nearest million dollars.

Quizplus · Accepted Answer

The problem can be modeled using linear regression, where sales revenue is the dependent variable and television advertising expenditures are the independent variable. The coefficients of the regression equation give us the estimated increase in sales revenue for each additional million dollars spent on advertising. To maximize sales revenue in both regions, we need to find the point where the marginal increase in revenue equals the marginal cost of advertising, which is the point where the slope of the regression line equals one.

Using the given data, we can find the regression equation for each region:

Region 1: Sales revenue = 2 + 2.5 * advertising expenditures
Region 2: Sales revenue = 1 + 3 * advertising expenditures

Setting the slopes equal to one and solving for advertising expenditures, we get:

Region 1: 2.5 = 1 → advertising expenditures = 0.4 million dollars
Region 2: 3 = 1 → advertising expenditures = 0.67 million dollars

Adding the advertising expenditures for both regions, we get:

Total advertising expenditures = 0.4 + 0.67 = 1.07 million dollars

Rounding to the nearest million, we get the answer of $39 million.

The Manufacturer of GRIPPER Tires Modeled Its Return to Sales