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Place value = 10 Face value = 2 Product = 20.
I can only assume that the term 'value' in product design holds the same meaning as it does in branding and advertising. Value is a measurement and indication of a product's intangible worth. A new product does not hold any tangible worth as it has no record of monetary success or market share etc., it can only be predicted. A product can be deemed to hold great value if it represents as something which has the potential to achieve great success - i.e. has a strong USP, offers great margins, is highly transferable, is greatly innovative etc. Value in product design can be obtained and increased by including/ emphasising/ exploiting aspects of the product that are likely to encourage purchase. This can be extended further by saying that a product, though may not sell very well, still holds great worth if it supports the brand by acting as an augmentation, facilitating brand strength and worth, thus a greater external success.
The value of product shipped by cereal manufacturers were $9.1 billion in 1997
The value of product shipped by cereal manufacturers were $11.4 billion in 2001
The cross product can be said to be a measure of the 'perpendicularity' of the vectors in the product. Please see the link.