We have $1000 to invest, and three possible investments - a stock index fund, a bond index fund, and a money market.. Average returns on the stock index fund, the bond index fund, and the money market fund are 8%, 5%, and 2% respectively.

Total investment in the stock index fund and the bond index fund should not exceed 80% of available funds. Total investments in the bond index fund and the money market fund should be at least 30% of the available funds. And investment in stock index fund should not exceed the sum of investments in the bond index fund and the money market fund.

To maximize our average return, how much should we invest in the stock market fund?

(Hint: decision variables are how much to invest in each of the three funds)