Using Python, suppose we have an investor that is trying to decide on investing $1000 between two securities (a and b). Both securities cost 10 dollars per unit. A year later security a and b will pay 30 dollars and 5 dollars, respectively in state u. And in state d, security a will pay 5 dollars, and security b will pay 12 dollars.

The state u is likely to occur with 30% probability while the state d is likely to occur with 70% probability. And the investor's utility function is u(w) = w ** 0.5 (square root of wealth).

How much money the investor should put into each security to maximize the utility?