48. A company runs a regression analysis to identify the impact of volume on demand, which can be shown in an equation as y = 50x + 110. Which volume is required to produce a demand of 10,510?
Answer: B
The volume required to produce a demand of 10,510 is 210.
To find the volume that results in a demand of 10,510, we can use the regression equation y = 50x + 110 and solve for x when y equals 10,510.
A) 208
While calculating the volume using the equation, substituting x = 208 yields a demand of 10,510, which is incorrect. Specifically, plugging in 208 results in a demand of 10,410, demonstrating that this option does not meet the required demand of 10,510.
B) 210
Substituting x = 210 into the equation gives y = 50(210) + 110 = 10,510. This calculation confirms that using a volume of 210 will produce exactly the required demand of 10,510, making this the correct choice.
C) 525,500
Using x = 525,500 in the equation results in an excessively high demand value of 26,275,110 (calculated as 50(525,500) + 110), which far exceeds the needed demand of 10,510. Therefore, this option is incorrect.
D) 525,610
Substituting x = 525,610 produces an even larger demand of 26,275,210 (50(525,610) + 110), which is not only incorrect but also significantly higher than the demand target of 10,510.
Conclusion
The only volume that accurately produces a demand of 10,510 is 210, as confirmed by substituting this value into the regression equation. All other options either fall short or exceed the required demand significantly, underscoring that Option B is the definitive correct answer.