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Breathe in oxygen, exhale carbon dioxide Run around and eat plants And dump fertilizer out the back Animals evolved (Congratulations, you were part of the solution) The solution worked With animals around, the excess oxygen was used up steadily, and massive res became rare But this solution did much more than solve the basic problem of eliminating excess oxygen It had a lot of what executives like to call added value According to the three key measures of value in the ecosphere: Biomass increased many thousand-fold The fertilizer dumped by the animals became soil, nourishing the growth of both plants and animals Biodiversity increased rapidly Plants evolved ways of avoiding being eaten, and ways of taking advantage of parts being eaten (such as pollination of owers and spreading of seeds through edible fruit) Animals diversi ed as they adapted to the changes in plants Stability increased.

Figure B-4

(9.13) A plot of Eq. (9.13) for conditions of CH/AkH = Cc/Akc = 1 is given in Fig. 9..5. Compare it with the curves of Fig. 9.4. The point of the foregoing analysis has been to demonstrate the nonlinear properties associated with heat transfer. Even under the most favorable conditions, manipulation of flow is far from sat isfactory for temperature control. There are practical considerations, too. Throttling of streams which may contain impurities (river water, for example) can cause deposits to accumulate, fouling the heat transfer surfaces. Furthermore, manipulation of flow causes variable loop gain through the variation of dead time. In the event that there is no alternative to the manipulation of flow, an equal-percentage valve characteristic should be chosen. Part of the stream whose temperature is to be controlled may be allowed to bypass the exchanger as shown in Fig. 9.6. But Fig. 9.3 indicates that

526 Worked-Out Solutions to Exercises: 11-19

Figure B-5

The excess accumulated oxygen decreased, and the new stable level of oxygen was optimized for both plants and animals The biosphere also got a new, higher level of atmospheric carbon dioxide and a more stable global temperature..

9 Figure B-5 shows the graph of the original relation with its domain restricted to the reals smaller than or equal to 2 ( gray curve) and its inverse (black curve) The curve for the inverse relation is a half-hyperbola that opens downward and intersects the y axis at (0, 2) A movable vertical line never intersects the black curve at more than one point Therefore, the inverse relation f 1 (x) = (4x 2 /9 + 4)1/2 is a true function of x 10 Figure B-6 shows the graph of the original relation with its range restricted to the nonnegative reals (pair of gray curves) and the graph of its inverse (pair of black curves) A movable vertical line never intersects the graph of the original restricted relation at more than one point, so it s a true function Whenever the movable vertical line intersects the graph of the inverse, that line crosses both curves On this basis, we know that the inverse of the original restricted relation is not a true function

13

2 2 4 6

What can we learn from nature s example In planning a system, de ne the niche. Look at all the inputs and outputs, and de ne functions that will add value to the business as a whole in important ways. It is not enough just to solve one problem. Likewise, we must design and build our products and services to t in with the whole organization (or our customers) and provide many bene ts, many kinds of value.

$1; 1 m1o FIG 9.5. h V a r i a t i o n f t e h e a t transfer coefficient with flow somewhat eases the nonlinearity of the process.

Figure B-6

13

The project life cycle is important enough that we have devoted Part Two of Project Management Demysti ed to it with one chapter for each stage. Here, we take a closer look at the stages and gates of the project and product life cycles.