solver problem with Stock portfolio

[lirongr1996]

Hi,
I am trying to optimize the stock portfolio.
I have 12 stocks and $ 1 million.
The constraints:
1. I need choose between 4-8 stocks to the portfolio.
2. The weights of the stocks will be between 0.1 to 0.4.
3. Sharpe ratio need will be small equal to 1.0
4. Will be at least 100000 cash
5. can be taken a loan up to 50

How can I make the solver choose 4-8 stocks with the constraint of the weights will be at least 0.1? That it will be zeros in some wieghts who do not in the portfolio.

I ave the constraints:
1. binary variable for each stocks.
2. variable for each stocks.
3. the constraints for choose between 4-8 socks with the binary variables.
4.The sum of the variables represent the weights will be 1
5. The variable represent the weights will be Small equal to the binary variables- I thought that will be help for fill zeros in the stocks that do not int the portfolio.
6. The sum of the variables for each stocks minus the variable of the cash will be small equal to milion and a half dollar.

Thank you for the help.

 

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