Problem 1 (35 pts) As a manager of a small business, you are considering to introduce a new product. The production requires a new machine. You figure out that you could buy it for $190,000, but the price could be in between $180,000 and $200,000. Because of the budget limitation you can only pay 60% of the machine price with your own saving. You will borrow the other 40% with an interest rate around 9% per year (but subject to change in between 8.5% and 10% ). The demand of this product is predicted to be 15,000 per year and but could be in between 14800 and 15500 . The unit price could be in between $2 and $3, and now you believe that $2.5 is a reasonable price right now. The raw material cost is estimated to be $0.9 but could be in between $0.5 and $1.2. The operation cost of the equipment is around $0.2 for one product but could be in between $0.1 and $0.25. The maintenance cost for this equipment is estimated to be $2000 per year but could be in between $1500 and $2300. Suppose you could always invest your cash in the money market that give a return at 8% per year for sure. Please do following analysis: a) Construct the Influence Diagram for this decision problem and identify the inputs and mathematic models that relate these inputs (decision variables) to the decision problem. (10) b) Construct the Tornado Diagram (10) c) Based on Tornado Diagram, identify two most sensitive variables, and do twoway sensitivity analysis based on these two variables. Illustrate your result in twoway sensitivity graph (10) d) Can you decide whether to invest after these analyses? If not, what to do next