1. This exercise is based on one in Hartman (2007). Apharmaceutical company needs to use a supercomputer to runsimulation models as part of its research on cures for AIDS,cancer, and other diseases. The firm expects to perform thousandsof simulation runs per year for the next 3 years. The firm canpurchase a supercomputer for $2.5 million; the annual operating andmaintenance costs are $200,000 per year, and the supercomputer canperform 15,000 runs per year. For every simulation run above 15,000in a year, the operating costs rise $1,000 per year to cover theneeded overtime. A second alternative is to outsource thesimulation runs to an IT firm that offers supercomputing serviceson demand. They will charge the pharmaceutical company $400 persimulation run. Consider a 3-year time horizon, and assume that thenumber of runs per year is the same every year. The firm is notsure how many simulation runs they will need to perform each year.What is the range of total cost if the number of simulation runsvaries from 10,000 to 20,000 runs per year? For what range ofactivity (number of simulation runs per year) is purchasing asupercomputer the lowest cost alternative?

2. Consider the supercomputer example from Exercise 1 above. Thefirm is not sure about some of the relevant costs. The followingprobability distributions reflect their beliefs about the uncertaincosts: the annual operating and maintenance costs are uniformlydistributed on the range [$150,000, $250,000]; the additionaloperating costs for simulation runs above 15,000 per year areuniformly distributed on the range [$500, $1500] (per run peryear). Use the method of moments to estimate the mean and varianceof the costs if the firm purchases the supercomputer and theyperform 20,000 runs per year. Use Monte Carlo sampling to estimatethe distribution of costs if the firm purchases the supercomputerand they perform 20,000 runs per year.