how can I answer part d

Consider a risky stock priced at $100 per share whose price in one year will take on the following set of possible outcomes: Assume an investor has an initial wealth of $300 and a logarithmic utility function. Use expected utility to determine whether or not the investor will purchase one unit of the risky stock. [5] c) Assume the investor is uncertain about the first and third probability values in the distribution of the future stock price i.e. the investor has the following information about the future stock price: Determine the minimum value of p at which the investor is indifferent between purchasing or not purchasing one unit of the stock. [5] d) Suppose the investor revises their estimates for the future prospects of the risky stock. The investor assumes the stock price in one year will be equal to one of the following two possible outcomes: Assume the investor can invest a proportion of their wealth in the risky asset and retain the remainder (to earn a risk-free rate of zero). Determine the optimal proportion by maximising the investor's expected utility. [7]