An investor is going to invest $$100$M$.$ The following investments are available: Bonds, home loans, hedge

funds and stock market with annual rate of returns $8\%,9\%,7\%$ and $11\%$ respectively. There are several

restrictions on investments:

$$ The amount invested in hedge funds should be at least equal to the amount invested in bonds.

$$ The amount invested in home loans should be less than or equal to the amount invested in stock

market and the amount invested in bonds.

$$ No more than $30\%$ of the total amount invested should be on stock markets.

Formulate an LP that will maximize the annual rate of return of the investor.