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

Minimum of 2M USD is required to be invested.

Explanation:

Chester's Elite product Cid Awareness = 72%

First 1M USD generates = 22% awareness

Second 2M USD generates = 23% awareness

Third 3M USD generates = 5%

1/3 of Cid's existing awareness is lost every year

if Cid Awareness = 72% this year.

Next Year it will be = 72-24 = 48%

Year after next year = 48-16 = 32%.

So,

we know that Agape's Awareness remains same next year = 77%.

So, Chester's Elite Product Manager should spend 2M USD in promotion in order to get ahead from Andrew's Agape Product.

Because by spending 2M USD Cid Awareness will become = 117% = 72 + 22 + 23.

So, after a year if it lost 1/3 then = 1/3 of 117 = 39

So, final awareness of Cid will be = 117-39 = 78%

And Andrew's Awareness will be = 77%

Hence, minimum of 2M USD is required to be invested.