Note: Problems $112$ are designed to give you practice in setting up a simulation model and demonstrating how random numbers can be used to generate values for the probabilistic inputs. These problems, which ask you to provide a small number of simulation trials, can be done with hand calculations. This approach should give you a good understanding of the simulation process, but the simulation results will not be sufficient for you to draw final conclusions or make decisions about the situation. Problems $1325$ are more realistic in that they ask you to generate simulation output$($s$)$ for a large number of trials and use the results to draw conclusions about the behavior of the system being studied. These problems require the use of a computer to carry out the simulation computations. The ability to use Excel will be necessary when you attempt Problems $1325\mathrm{.}1.$ Consider the PortaCom project discussed in Section $16\mathrm{.}1.$a$.$ An engineer on the product development team believes that first$-$year sales for the newprinter will be $20,000$ units. Using estimates of $$45$ per unit for the direct labor cost and $$90$ per unit for the parts cost, what is the first$-$year profit using the engineers sales estimate?b$.$ The financial analyst on the product development team is more conservative, indicating that parts cost may well be $$100$ per unit. In addition, the analyst suggests that a sales volume of $10,000$ units is more realistic. Using the most likely value of $$45$ per unit for the direct labor cost, what is the first$-$year profit using the financial analysts estimates?c$.$ Why is the simulation approach to risk analysis preferable to generating a variety of what$-$if scenarios such as those suggested by the engineer and the financial analyst?