Typically,the sales volume declines with an increase of a product price.It has been observed,however,that for some luxury goods the sales volume may increase when the price increases.The following Excel output illustrates this rather unusual relationship. For which of the following two prices are the sales predicted by the quadratic regression equation equal 1700 units?
A) 60.51 and 150.15
B) 61.51 and 151.15
C) 62.51 and 152.15
D) 63.51 and 153.15

Question

Typically,the sales volume declines with an increase of a product price.It has been observed,however,that for some luxury goods the sales volume may increase when the price increases.The following Excel output illustrates this rather unusual relationship.  For which of the following two prices are the sales predicted by the quadratic regression equation equal 1700 units?
A) 60.51 and 150.15 
B) 61.51 and 151.15 
C) 62.51 and 152.15 
D) 63.51 and 153.15

Quizplus · Accepted Answer

From the Excel output, we know that the quadratic regression equation is:
Sales = -144.9 + 49.1*Price - 0.346*Price^2
To find the prices at which sales are predicted to be 1700 units, we need to set the equation equal to 1700 and solve for Price:
-144.9 + 49.1*Price - 0.346*Price^2 = 1700
0.346*Price^2 - 49.1*Price + 1844.9 = 0
Using the quadratic formula, we get:
Price = (49.1 ± sqrt(49.1^2 - 4*0.346*1844.9)) / (2*0.346)
Price ≈ 61.51 or 151.15
Therefore, the answer is B, because those are the two prices at which sales are predicted to be equal to 1700 units.

Typically,the Sales Volume Declines with an Increase of a Product