What is right # of funds in a portfolio

What is the right number of funds in an optimal portfolio? There are three major factors determine the right number, available investment assets (or portfolio size), Minimum initial investment size and additional investment size for each fund, and minimum exchange size or trading size relative to exchange fees or trading fees.

In elsewhere, I have estimated the expected trading return is a linear function of standard deviation over expected return of each fund. Sharpe has proposed that the portfolio risk-adjusted return can be measured by Sharpe Ratio which is the expected return divided by standard deviation. So an optimal portfolio should have the minimum risk-adjusted portfolio return and at the same time the maximum volatility for each fund.

Now we have a conflict of interest. On one side, for each fund, we are expecting high standard deviation. On another side, we are expecting low standard deviation for the entire portfolio. Solving this conflict of interests is the entire art of portfolio management.

Tobin once proposed a Tangent portfolio as the optimal portfolio. A balanced combination of risk-free asset with the risky tangent portfolio should lead us to a maximum Sharpe Ratio. What should be appropriate weights for the risk-free asset and the risky tangent portfolio?