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Algebra Connections Chapter 3 Answers

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    In addition, the Japanese data show that they have a high preference for things American, and, as you know, we are a classic American company. European competitors are virtually unrecognized, and other Far Eastern competitors are perceived to be of...

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    Of course, there is a lot of uncertainty in the sales volumes we are planning. The pricing will cover some of the uncertainty but is still less than comparable quality goods already being offered in Japan. We have established long-term relationships...

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    By contrast, we have simply mailed them the same catalog we use in the U. They prefer our broader assortment by a ratio of , even though they don't buy most of the products. As the competitors figured, sales are focused on outerwear and knits, but we are getting more sales, apparently because they like looking at the catalog and spend more time with it.

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    Again, we need further testing. Another hypothesis is that our brand name is simply better known. We do not expect this trend to hold in a general mailing. If we can get them to order by phone, we can correct the errors immediately during the call. Of course, paper and postage costs increase as a consequence of the larger format catalog. On the other hand, there are production efficiencies from using the same version as the domestic catalog. Net impact, even factoring in the error rate, is a significant sales increase. On the other hand, most of the time, the errors cause us to ship the wrong item which then needs to be mailed back at our expense, creating an impression in the customers that we are not well organized even though the original error was theirs. Assuming—we need to test this—that the length of time they keep the catalog is proportional to sales volumes, this is good news.

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    We need to assess the overall impact carefully, but it appears that there is a significant population for which an English-language version would be very profitable. Jennifer, what do you have on customer research? We have learned that Japan is very fad-driven in apparel tastes and fascinated by American goods. We expect sales initially to sky-rocket, then drop like a stone. Later on, demand will level out at a profitable level. The graphs on page 3 [ Figure ] show demand by week for weeks, and we have assessed several scenarios. They all show a good underlying business, but the uncertainty is in the initial take-off. The best data are based on the Italian fashion boom which Japan experienced in the late 80s.

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    It is not strictly analogous because it revolved around dress apparel instead of our casual and weekend wear. It is, however, the best information available. Japan "Our effectiveness in positioning inventory for that initial surge will be critical to our long-term success. There are excellent data—supplied by MITI, I might add—that show that Japanese customers can be intensely loyal to companies that meet their high service expectations. That is why we prepared several scenarios. Of course, if we position inventory for the high scenario, and we experience the low one, we will experience a significant loss due to liquidations. We are still analyzing the long-term impact, however. It may still be worthwhile to take the risk if the 2-year ROI 1 is sufficient.

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    Seventy percent are small and medium. This will be a challenge to manage but will save a few bucks on fabric. We are still researching color choices, but it varies greatly for pants versus shirts, and for men versus women. We are confident we can find patterns, but we also know that it is easy to guess wrong in that market. If we guess wrong, the liquidation costs will be very high. They don't like to order by phone. Perhaps the most important is one not often mentioned, and that is the ability to convert an important business question into an appropriate mathematical one, to solve the mathematical problem, and then to explain the implications of the solution for the original business problem.

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    This ability to inhabit simultaneously the business world and the mathematical world, to translate between the two, and, as a consequence, to bring clarity to complex, real-world issues is of extraordinary importance. In addition, the participants in this conversation understood and interpreted graphs and tables, computed, approximated, estimated, interpolated, extrapolated, used probabilistic concepts to draw conclusions, generalized from Page 22 Share Cite Suggested Citation:"Part One: Connecting Mathematics with Work and Life.

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    Another very important aspect of their work was that they identified additional questions, and they suggested ways to shed light on those questions through additional analysis. There were two broad issues in this conversation that required mathematical perspectives. The first was to develop as rigorous and cost effective a data collection and analysis process as was practical. It involved perhaps 10 different analysts who attacked the problem from different viewpoints. The process also required integration of the mathematical learnings of all 10 analysts and translation of the results into business language that could be understood by non-mathematicians. The second broad issue was to understand from the perspective of the decision-makers who were listening to the presentation which results were most reliable, which were subject to reinterpretation, which were actually judgments not supported by appropriate analysis, and which were hypotheses that truly required more research.

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    In addition, these business people would likely identify synergies in the research that were not contemplated by the analysts. These synergies need to be analyzed to determine if—mathematically—they were real. The most obvious one was where the inventory analysts said that the customers don't like to use the phone to place orders. This is bad news for the sales analysts who are counting on phone data collection to correct errors caused by language problems.

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    Of course, we need more information to know the magnitude—or even the existance—of the problem. In brief, the analyses that preceded the dialogue might each be considered a mathematical task in the business world: A cost analysis of store operations and catalogs was conducted using data from existing American and possibly other operations. Customer preferences research was analyzed to determine preferences in quality and life-style. Cultural differences were recognized as a causes of analytical error. Careful analysis required judgment. In addition, sources of data were identified in the U. A search was conducted for other comparable retail experience, but none was found. On the other hand, sales data from car parts and computers were assessed for relevance. Rates of change are important in understanding how Japanese and American stores differ.

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    Sample size and error estimates were mentioned. Key drivers of behavior lifestyle, income, education were mentioned, but this list may not be complete. What needs to be known about these families to predict their buying behavior? What does "lifestyle" include? How would we quantify some of these variables? A hypothesis was presented that catalog size and product diversity drive higher sales. What do we need to know to assess the validity of this hypothesis?

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    Another hypothesis was presented about the quality of the translation. What was the evidence for this hypothesis? Is this a mathematical question? Sales may also be proportional to the amount of time a potential customer retains the catalog. How could one ascertain this? Despite the abundance of data, much uncertainty remains about what to expect from sales over the first two years. Analysis could be conducted with the data about the possible inventory consequences of choosing the wrong scenario. One might wonder about the uncertainty in size scales.

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