An investor with initial wealth of W0 > 0 wants to maximise expected utility of her end of period wealth, W1 by investing in one risky asset and one risk free asset. The risk free rate of return is three percent. The return on the risky asset is 8% with probability 0.7 and 3% with probability 0.3. The utility function of the investor u(x) = ln(x). Note that the investor is seeking to maximise Eu(W1).

Set up the optimization problem?

I think the problem may include the use of lambda but not 100% sure?