Question $2$:

In the start$-$up of a new manufacturing plant, considerable difficulty was experienced with a lime slaking unit. At a meeting to discuss the problem the following seven variables were proposed as being possibly responsible.

$\backslash$table$[[$Variable$,+,-],[$A Lime particle size,big,small$],[$B Lime type,hardburned,softburned$],[$C Lime$/$water ratio,$200$g$/1,100$g$/1],[$D Stirring rate,fast,slow$],[$E Water used for slaking,seawater,well water$],[$F Slaking water temperature,$60\backslash$deg C$,20\backslash$deg C$],[$G Additives,$1\%$ Ethanol,none$]]$

In the list above, the plus version corresponds to the usual operating condition and the minus version to a possible change.

A $2^{7-4}$ saturated experimental design of resolution III was carried out with the results given below:

$\backslash$table$[[,$Variable,$],[$Run$,$A$,$B$,$C$,$D$,$E$,$F$,$G$,$Response$],[1,-,-,-,-,+,+,+,7\mathrm{.}50],[2,+,-,-,+,-,-,+,15\mathrm{.}05],[3,-,+,-,+,-,+,-,15\mathrm{.}40],[4,+,+,-,-,+,-,-,7\mathrm{.}10],[5,-,-,+,+,+,-,-,6\mathrm{.}60],[6,+,-,+,-,-,+,-,15\mathrm{.}90],[7,-,+,+,-,-,-,+,12\mathrm{.}70],[8,+,+,+,+,+,+,+,8\mathrm{.}70]]$In each run a sample of the slaked lime produced was titrated with $8MHCl$ in an autotitrator

operating as a $pH$ stat set to $pH$ of $7\mathrm{.}8.$ The response measured was the volume of $HCl$

consumed in a standard time $-$ the larger the value the better the quality of the slaked lime$.$

A second set of experiments was run, with the contrast signs reversed, yielding the following

results:

Calculate the main effects of the variables, unconfounded with two$-$factor interactions and

comment upon the results.