The Sharpe Ratio is simply the slope of the line that connects a portfolio and the Risk Free Rate. The line with the highest Sharpe Ratio is the one that connects Optimal Portfolio and the Risk Free Rate. The mathematical formula for the Sharpe Ratio is:

[ (Return – Risk Free Rate) / Standard Deviation ]

Basically, it is the return for taking risk divide by the risk taken. Logically, if we want to maximize the return / risk ratio, we maximize the Sharpe Ratio.