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$)$ comprised of level $1$ of surfactants, level $6$ of solubility, level $3$ of color, and level $1$ of scent.

$[100000000010000001001000]$

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 $80$ respondents are given in the file dishsoap.

Click on the datafile logo to reference the data.

DATA $\sqrt[\phantom{2}]{f}$ile

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.

Enter the levels of the new product for four attributes. Give your answers as whole numbers.

Note: It might take up to $10$ minutes for Excel Solver to obtain optimal solution.

Surfactants: level

Solubility: level

Color: level

Scent: level

What is the optimal objective function value?

The new product's utility exceeds the status quo utility for out of the $80$ respondents