Corner Portfolio Question someone, provide, required, why

Carson

Hypothetical question....looking for someone who can provide the answer. (Paraguay I am looking at you!)

So you have a required return of 9% and you have three corner portfolios:

Portfolio 1: Return = 8%, Sharpe = 0.7
Portfolio 2: Return = 10%, Sharpe = 0.8
Portfolio 3: Return = 12% , Sharpe = 1.1

According to Schweser the answer would be to take the corner portfolios 1 & 2 to solve for the answer which would be a 50% weight in each.

Now my answer is, why are you not taking portfolio 3 & 1 since portfolio 3 has a much better risk adjusted return? The weight being 75% from port 1 and 25% from port 3.

Thanks in advance guys!