Question 1. With 50 large trucks available for rental to industrial contractors, Freddy is offering his Pepperdine TruckRental Company for sale at a price of $1,000,000. Freddy wants you to develop a three-year economic analysis to assist buyers in evaluating the company. The company's property taxes are $35,000 per year and are expected to grow at an annual rate of 4%. Freddy currently spends $4,800 per year per truck to maintain and administer the fleet. Maintenance and administrative costs are largely fixed and independent of truck rental rates. Administrative and maintenance costs are expected to increase by 7 percent per year. Currently, Freddy rents his trucks for $1,000 per month each. About 60 percent of the trucks are rented each month but Freddy believes demand for his trucks is highly elastic. His experiments indicate that the percentage of the fleet rented each month increases by 7 percent for each $100 per truck per month reduction in the rental price. For example, at $600 per month, he expects that 88 percent of histrucks would be rented. He also believes rental prices can be increased 9 percent in years two and three without affecting the fleet rental percentage established during the first year. That is, in year 2 a $654 rental price (a 9% increase) will result in a rental rate of 88%. At the end of three years, Freddy assumes the buyer will resell the truck rental business for three times the revenue earned in year three. Until the end of the third year, the fleet will remain constant and no trucks will be bought or sold. Define cash flow as revenue minus expenses, and ignore depreciation and income taxes. Assume that cash flow in year three includes the proceeds from the sale of the business at the end of the year and that year one's cash flow includes the purchase price at the beginning of the year. Define overall investment profit as the net present value (NPV is one of Excels built in functions use Excels help facility to confirm the calculations used with the NPV function) of the cash flows over the three years, assuming an annual discount rate of 10%. Questions:

1.Construct an influence diagram for your analysis, labeling the decision variables, the key parameters, and the performance measures. In addition, clearly state all assumptions you make. All assumptions that you make must be reasonable. (20 pts)

2.Provide the standard form for the mathematical model. (20 pts)

3.Use your influence diagram and standard form to construct a model that computes NPV for this investment assuming the term begins with the current rental price of $1000. (30 pts) Follow the guidelines when building the analytical model. (10 pts)

4.Use Solver to find the optimal rental price in year 1 given that the rental price will increase by 9 percent annually. (10 pts)

5.Is this a linear optimization or a nonlinear optimization problem? Explain why. (10 pts)