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The question now is, at what rates can we sell 21 single rooms and 14 double rooms (at a price $10 higher than the singles) so that total revenue is $1,450 Expressed arithmetically, this becomes (with x the unknown single rate): 21x 21x 14(x 14x $10) $140 35x 35x x x $1,450 $1,450 $1,450 $140 $1,310 $1,310 / 35 $37.43

rates for adding service charges for out-of-state long-distance telephone service. The telephone department became a very pro table area in the hotel business. Since all phone calls are charged to the guest folio, an accurate accounting of the charges is necessary. In a hotel with a call-accounting system that interfaces with a property management system, this tally is electronically obtained.

Supply Chain Division Scenario A Distribution Manager for the North Region requires a supply chain dashboard. This manager requires the weekly sales numbers for each item (or stock keeping unit, SKU) with variance to indicate anticipated adjustment in the inventory. The requirements include quarterly tracking of inventory turns and gross margin for the region as compared to the overall company. Also, there is a need for real-time days of supply and inventory turns for each product category with further drill-down into each item. The design of an effective dashboard in this scenario would require application of appropriate chart types such as pie, trend line, bar/column charts, and summary tables. For example, weekly sales by SKU may be in a table format because a large number of SKUs need to be displayed. Negative variances may be highlighted in red to get a viewer s immediate attention. Quarterly inventory turn tracking may be displayed as a trend line, while the gross margin may be juxtaposed on the same time frame as a column chart with a different scale. Days of supply for different categories may be displayed as a small table, which may be drilled down to similar metrics at the individual SKU level within each category (see Exhibit 9.9).

the maximum ow across any cut set cannot be greater than the sum of the capacities of the cut edges Thus, minimizing the maximum ow across cut sets yields an upper bound on the capacity of the network The Ford Fulkerson theorem [214] shows that this capacity can be achieved The theory of information ow in networks does not have the same simple answers as the theory of ow of water in pipes Although we prove an upper bound on the rate of information ow across any cut set, these bounds are not achievable in general However, it is gratifying that some problems, such as the relay channel and the cascade channel, admit a simple max- ow min-cut interpretation Another subtle problem in the search for a general theory is the absence of a source channel separation theorem, which we touch on brie y in Section 1510.

A complete theory combining distributed source coding and network channel coding is still a distant goal In the next section we consider Gaussian examples of some of the basic channels of network information theory The physically motivated Gaussian channel lends itself to concrete and easily interpreted answers Later we prove some of the basic results about joint typicality that we use to prove the theorems of multiuser information theory We then consider various problems in detail: the multiple-access channel, the coding of correlated sources (Slepian Wolf data compression), the broadcast channel, the relay channel, the coding of a random variable with side information, and the rate distortion problem with side information We end with an introduction to the general theory of information ow in networks There are a number of open problems in the area, and there does not yet exist a comprehensive theory of information networks.

Soft sensors can infer important process variables (called outputs) from available hardware sensors (called inputs). Usually the outputs are measured infrequently by laboratory analysis, material property tests, expensive gas chromatograph analysis, and so forth. Very often the output measurement is performed of ine and then introduced into the online process monitoring and control system. It is assumed that soft sensor inputs are available online, either from cheap hardware sensors or from other soft sensors. Different inference mechanisms can be used for soft sensor development. If there is a clear understanding of the physics and chemistry of the process, the inferred value can be derived from a fundamental model. Another option is to estimate the parameters of the fundamental model via Kalman lter or extended Kalman lter. There are cases when the input output relationship is linear and can be represented either by linear regression or by multivariate model; additionally, Kalman lter assumes Gaussian distribution and stationary signals (Kalman, 1960). The most general representation of the soft sensor, however, is a form of nonlinear empirical model, and the signal is, generally, nonstationary.