I need help with following parts relating to this question:

1. The manufacturer has collected monthly data on past market prices of widgets. Suppose that all annual price change can be assumed to be drawn from a normal distribution. Choose and fully explain the appropriate model for simulations and simulate prices, outputs and profits.

2. If the company evaluates the project by discounting expected profits and the cost of capital is 10%, what is the NPV of the project? All cash-flows are assumed to be received at year end. Provide a justification for your logic.

3. What is the probability that the plant will produce at capacity in Year 2? Suppose that the company can buy extra equipment that would expand the capacity to 6,800,000 units. What is the maximum amount that the company will be prepared to invest in extra equipment? Explain your approach to answering this question.