If is the number of shares she should purchase of the internet fund and is the number of shares she should purchase of the index fund, then is the amount she should invest in the internet fund and is the amount she should invest in the index fund.

So, you were given proportions of those amounts. You were told that "the dollar amount she invests in the index fund relative to the Internet fund should be at least one-third" which means that she wants to invest at least one third as much in the internet fund that she is investing in the index fund: .

Then "she should not invest more that twice the amount in the Internet fund that she invests in the index fund" means the amount she spends on the internet fund should be less than or equal to twice the amount she spends on the index fund: .

So, now you have the three constraints:

(I combined two of the constraints into one)

I would recommend looking in your book to see how to solve this system graphically.