1. Unlike the projective case, ideal points form a boundary, not a submanifold. 2. Increased product variety provides consumers with offerings nearer their ideal points . 3. Areas without ideal points are sometimes referred to as demand voids. 4. Some maps plot ideal vectors instead of ideal points . 5. Many perceptual maps also display consumers ideal points . 6. Human tears have a pH of 7.4, making this an ideal point to set a pool. 7. In the 19th century, the isolation made it an ideal point for the meetings of pugilists. 8. His book preaches the use of probabilities to determine ideal points to begin building a position. 9. In hyperbolic geometry an "'ideal triangle "'is a hyperbolic triangle whose three vertices all are ideal points . 10. The next diagram shows a study of consumers ideal points in the alcohol / spirits product space.
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