Problem 4 (15 points) Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a coat of $130 per room The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be reserved at a cost of $230 per room a. Use simulation with @ RISK to determine the number of rooms that should be reserved to minimize the expected cost to the AMA. Try values from 4100 to 4900 in increments of 100. (If you wish, you can use the shell file Sb15_29.xlex or create your own) Report the average cost for each of the nine possible values. b. Redo part (2) for the case where the number attending has a triangular distribution with minimum value 2000. maximum value 7000, and most likely value 5000. Report the average cost for each of the nine possible values. c. Does using triangular distribution change the results from part (2) considerably? Problem 5 (15 points) A hardware company sells a lot of low-cost, high-volume products For one such product, it is equally likely that annual unit sales will be low or high. If sales are low (60,000), the company can sell the product for $10 per unit. If sales are high (100,000), a competitor will enter and the company will be able to sell the product for only $8 per unit. The variable cost per unit hee a 25% chance of being $6, 2 50% chance of being $7.50, and a 25%% chance of being $9. Annual fixed costs are $30,000. a. Run a simulation with @RISK and report the company's expected annual profit. (If you went, you can use the shell file Sh15_32xlax or create your own.) b. Find a 90%% interval for the company's annual profit, that is, an interval such that about 90% of the actual profits are inside it. c. Now suppose that annual unit sales, variable cost, and unit price are equal to their respective expected values - that is. there is no uncertainty. Determine the company's annual profit for this scenario d. Can you conclude from the revolts in parts (a) and (c) that the expected profit from a simulation is equal to the profit from the scenario where each input assumes its expected value? Explain. Problem 6 (20 point:) Consider the new car simulation from Example I in lecture notes "Simulation Models - Part 3"_ (2) Change the simulation model by introducing uncertainty into the fixed development cost. Let it be triangularly distributed with parameters $600 million, $650 million, and $850 million. (You can check that the mean of this distribution is $700 million, the same as the cost given in the example ) Comment on the differences between your output and those in the example Would you may these differences are important for the company? (b) Rerun the simulation from Example 1, but now use the RiskSimtable function appropriately to simulate discount rates of 5%%. 7.5%, 10%%, 12.5%, and 15%. Comment on how and why the NPV changes as the discount rate changes
