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8 The dashed gray curves in Fig B-19 are the graphs of y = ln x and y = log10 x The portions of these curves below the x axis (that is, where y < 0) are cut off here, because we haven t included any of the negative y axis But the function values are still there, of course! We want to graph the product function y = (ln x)(log10 x) When we input several values for x, use a calculator to obtain the outputs, plot the points, and then connect the points by curve fitting, we get the solid black curve The domain of this product function is the set of all positive reals, and the range is the set of all nonnegative reals 9 Figure B-20 shows the same graphs as Fig B-18 Here, the x axis is logarithmic, spanning the two orders of magnitude from 01 to 10 The dashed gray lines are the graphs of y = ln x and y = log10 x The solid black line is the graph of the sum function y = ln x + log10 x

14

The project moves ahead as each stage feeds into the next. However, it is important to realize that gates serve a genuine function. We cannot assume a project should go ahead. If our initial evaluation was wrong, or if the situation changes, then the project may be of no value, or of less value than the cost, to the customer. In that case, it is best to cancel the project. Of course, the sooner the project is cancelled, the better, because it means less wasted time and money. That is why there are three gates during the planning stage. Project cancellation does not mean failure for the manager or the team. Failure in business comes from wasting time or money. If the situation changes and the project is not needed, it is better to stop sooner, so that

Figure B-20

03 0 1 3 10 x

1 0 . 1 The reaction whose characteristics appear in Fig. 10.2 is to be conducted Temperature at 50 percent conversion with V/F = 1 hr in a back-mixed re&ctor. is to be controlled at 230 F by manipulation of coolant temperature. Feed is preheated to reaction temperature. What is the lowest coolant temperature that will ensure st,ability in manual control 10.2 For the same reactor, the heat of reaction is 5000 Btu/lb, F is 4,000 lb/hr, and r. is 0.2. Coolant temperature required for control is 190 F. The

10 Figure B-21 shows the same graphs as Fig B-19 In this coordinate system, the x axis is logarithmic, spanning the single order of magnitude from 1 to 10 The y axis is linear, spanning the values from 0 to 25 The dashed gray lines are the graphs of y = ln x and y = log10 x The solid black curve is the graph of the product function y = (ln x)(log10 x) Figure B-21

we do not waste further money. This can be hard to do if the team, the customer, and others are invested in the project. Gates help. Each gate is a chance to ask: What is best for the company right now But let us turn our attention to success. In 2 we said that a process can succeed if we have the right resources and tools. The following chapters de ne everything we need to succeed in each stage of the project. Each stage is thought of as a process with a beginning, a middle, and an end. And, for each stage, we provide: Key points, where we discuss the most important issues for each stage. Resources, where we discuss what you need to complete the stage. Roles, where we de ne who does what. Input, where we describe the information and things that we have at the start of the stage. From the second stage on, the inputs of each stage are the outputs of the prior stage, plus the approval given at the gate. Process, the work the project manager and the team do during the stage. Output, the end results of the stage that go through the gate. Key tools for the stage, including forms, templates, and processes. Key concepts for the stage, a review of what matters most for you, your team, and your customer. Our case study, building a home theater system, illustrates important ideas and tools from each stage. Your project for learning, where you apply the tools to your project, learn the tools, and move your project towards success. Questions for learning.

x 1 3 10

546 Worked-Out Solutions to Exercises: 11-19