Question

Baldwin's Elite product Best has an awareness of 72%. Baldwin's Best product manager for the Elite segment is determined to have more awareness for Best than Andrews' Elite product Attic. She knows that the first $1M in promotion generates 22% new awareness, the second million adds 23% more and the third million adds another 5%. She also knows one-third of Best's existing awareness is lost every year. Assuming that Attic's awareness stays the same next year (77%), out of the promotion budgets below, what is the minimum Baldwin's Elite product manager should spend in promotion to earn more awareness than Andrews' Attic product?

Select: 1
a. 3M
b. 1M
c. Nothing
d. 2M

Answer 1

The minimum Baldwin's Elite product manager should spend in promotion to earn more awareness than Andrews' Attic product is $2M.

Step-by-step explanation:

To calculate how much the Baldwin's Elite product manager should spend in promotion to earn more awareness than Andrews' Attic product, we need to consider the awareness increase from the promotion budget and the decrease in awareness over time. The promotion budget is divided into three segments, and each segment contributes a certain percentage increase in awareness. The first $1M generates 22% new awareness, the second million adds 23% more, and the third million adds another 5%. One-third of Best's existing awareness is lost every year.

Let's start by calculating the awareness increase from the promotion budget. Assuming Baldwin's Elite product manager spends $x million in promotion:

1. First million: $x * 0.22
2. Second million: $x * 0.23
3. Third million: $x * 0.05

Next, we need to take into account the decrease in awareness over time. One-third of Best's existing awareness is lost every year. So, the total awareness increase will be:

Awareness Increase = Promotion Budget + (Promotion Budget * 0.22) + (Promotion Budget * 0.23) + (Promotion Budget * 0.05) - (Best's awareness * (1/3))

Since the goal is to have more awareness than Attic's 77%, we can set up an equation:

Promotion Budget + (Promotion Budget * 0.22) + (Promotion Budget * 0.23) + (Promotion Budget * 0.05) - (Best's awareness * (1/3)) > Attic's awareness

Simplifying the equation and substituting the given values, we can solve for the minimum promotion budget required:

$x + (0.22x) + (0.23x) + (0.05x) - (0.72 * (1/3)) > 0.77

$x + 0.22x + 0.23x + 0.05x - 0.24 > 0.77

0.50x - 0.24 > 0.77

0.50x > 1.01

x > 2.02

Therefore, the minimum Baldwin's Elite product manager should spend in promotion to earn more awareness than Andrews' Attic product is $2M.