Alice is an investor. She has $100 to invest in the Wonderland stock market which has three stocks to invest in: Wheat, Corn, Tea. Being an economy based mainly on agriculture, the return of the investment in Wonderland depends on the weather condition and the availability of water. The weather is either good with probability or bad (each happens with equal probability), and water is either enough or not (each happens with equal probability). The weather condition and the availability of water are not related (they have independent probability distributions). She only cares about her return and is to decide to invest $100 in one of the stocks. Her payoffs are as follows.

1. If the weather is good and there is enough water: then the rate of return of Wheat is 30%, Corn is 10% and Tea is 30% (that is, she receives $120 if she invests in Wheat, $110 if she invests in Corn, and $130 if she invests in Tea);
2. If the weather is good and there is not enough water: then the rate of return of Wheat is 20%, Corn is 10% and Tea is 20%;
3. If the weather is bad and there is enough water: then the rate of return of Wheat is 10%, Corn is 20% and Tea is 5%;
4. If the weather is bad and there is not enough water: then the rate of return of Wheat is 0%, Corn is 5% and Tea is 0%;

Answer the following questions.

1. (a)(1 mark) Formulate Alice's problem as a decision problem under uncertainty.
2. (b)(2 marks) Does Alice have and weakly or strongly dominated action? Explain.
3. (c)(2 marks) Which stock is the best choice for Alice? (Hint: Compare her expected utilities.)
4. (d)(1 mark) If Alice is allowed to divide $100 among the three stocks, will she choose to do so,
5. or will she continue to invest only in one stock? Explain.