In this report, a problem of classifying eight-line arrangements on the real projective plane is discussed. By using the combinatorial geometric method of finding transversals for all given segments, all possible eight-line arrangements have been generated from the three sets of 14 kinds of samples of seven-line arrangements, which are different each other. As a result, 135 kinds of eight-line arrangements have been observed.

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Office employee's dining rooms and other B&I (Business & Industry) foodservices have been a driving force behind the foodservice industry in Japan since the latter half of the 1980s, and the most popular style of operation for these facilities is the “cafeteria.”We sampled and analyzed 55 business locations and 98 foodservice outlets in the central metropolitan area in Tokyo, and ca me up with the standard features visible in the design of today's B&I foodservice facilities. Standard design features were studied from the following five perspectives: (1) style of foodservice outlet operation; (2) shape of cafeteria lanes; (3) length of cafeteria lanes; (4) distribution of facility area; and (5) worker productivity. At the same time, we studied the positioning of these standard features in relation to customer preference and selection Kansei, and to business Kansei aimed at achieving profitability for the foodservice operator. The results of this study, in order of the items listed above, were as follows:
(1) Regarding design value for cafeteria-style operations, based on customer preference and selection Kansei, up to 1, 500 servings are effective.(2) Regarding design value for straight cafeteria lanes (or variations), based on customer preference and selection Kansei, up to 1, 000 servings is effective.(3) Regarding design value related to the length of cafeteria lanes, based on a mutual b alance of customer preference and selection Kansei factors, the proportion of servings to lane length is a maximum of 20m for up to 1, 000 servings, and remains at 20m for up to 2, 000 servings. Furthermore, in the case of up to 2, 000 servings, it could be said that there is a menu correlation defined as [1 menu item = 1 meter of lane length].(4) Regarding the features of area distribution of facility in a cafeteria-style operation, once 1, 000 servings are exceeded, there is no correlation between the number of servings and the area of the kitchen and storerooms.(5) Regarding worker productivity, productivity in foodservice operations where the scale does not exceed 1, 000 servings falls by about 50% compared to operations in which the scale is 1, 000 servings or more. From these results, we confirmed that in terms of the correlation between dining room area and food preparation area as listed in conventional compilations of construction design materials and other sources, at the very least it will be necessary to incorporate as a variable the number of servings provided. We can anticipate that in thAe future, the standard features of scale (area), which are representative of the “hard”aspects of B&I foodservice facilities, will conform to the operation format, which represents the “soft”aspects of these facilities.

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