Question

Digby's Elite product Dim has an awareness of 72%. Digby's Dim product manager for the Elite segment is determined to have more awareness for Dim than Andrews' Elite product Apple. 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 Dim's existing awareness is lost every year. Assuming that Apple's awareness stays the same next year (77%), out of the promotion budgets below, what is the minimum Digby's Elite product manager should spend in promotion to earn more awareness than Andrews' Apple product

Answer 1

$2 million

Step-by-step explanation:

The first $1 million will increase awareness to 72% x (1 + 22%) = 87.84%

But 1/3 is lost every year, so awareness will be 87.84% - 72%/3 = 63.84%.

It needs to spend at least $2 million:

Awareness increases to [72% x (1 + 22%) x (1 + 23%)] - 72%/3 = 84.04%

the awareness level will be higher than the 77% threshold.