This exercise is based on one in Hartman $(2007).$ A pharmaceutical company needs to use a supercomputer to run simulation models as part of its research on cures for AIDS, cancer, and other diseases. The firm expects to perform thousands of simulation runs per year for the next $3$ years. The firm can purchase a supercomputer for $$2\mathrm{.}5$ million; the annual operating and maintenance costs are $$200,000$ per year, and the supercomputer can perform $15,000$ runs per year. For every simulation run above $15,000$ in a year, the operating costs rise $$1,000$ per year to cover the needed overtime. A second alternative is to outsource the simulation runs to an IT firm that offers supercomputing services on demand. They will charge the pharmaceutical company $$400$ $$200$ per simulation run. Consider a $3-$year time horizon, and assume that the number of runs per year is the same every year. The firm is not sure how many simulation runs they will need to perform each year. What is the range of total cost if the number of simulation runs varies from $10,000$ to $20,000$ runs per year? For what range of activity $($number of simulation runs per year$)$ is purchasing a supercomputer the lowest cost alternative? $($Hint: Don't use random numbers for this simulation. Instead, create your cost model and vary the input from $10,000$ to $20,000$ runs in increments of $10$ runs, then plot the resulting cost and analyze.$)$