Wegryn Consumer Goods (WCG) is considering entering the dish soap market with a new product it has yet to design. Using conjoint analysis, WCG has estimated part-worth utilities for 80 survey respondents for the following four attributes for dish soap:

● Surfactants—chemicals that help suspend the oils and residue on dishes (5 levels)

● Solubility—how quickly a soap dissolves in water (10 levels)

● Color—the color of the soap (5 levels)

● Scent—the aroma of the soap (4 levels)

WCG has also collected the profile of the status quo product for each of the respondents in the form of a binary vector of length 24.

For example, the following vector indicates that this respondent is currently using a product comprised of level 1 of surfactants, level 6 of solubility, level 3 of color, and level 1 of scent.

The utility of the status quo product for each respondent can be obtained by adding up the part-worth’s of the levels indicated for the status quo product.
The part-worth utilities and the status quo vector for each of the 110 respondents are given in the file dishsoap.
WCG wants to construct a new dish soap product so that the new product is more valuable than the status quo product for the maximum number of respondents. What is the optimal objective function value?

Transcribed Image Text:

[10000000001000000 100 1000]