4. Consider an investor whose utility function over money is u(w)= 2w?. The investor can invest in a riskless asset that returns 1 (gross return per 1 invested) for sure, or a risky asset that returns 1.4 with probability and 0.8 with probability . (a) Suppose the investor's initial wealth is 1000. Letting x denote the amount invested in the risky asset, write the investor's expected utility as a func- tion of x. (b) Find the optimal amount to invest in the risky asset.