$4\mathrm{.}4[$Alphen$.$xlsx$]$ Alphen is an Austrian company producing yoghurt. In order to produce a new product for coeliacs,

the company has to select a supplier of goat's milk $($which does not contain gluten$).$ The company has decided to consider

two selection criteria: the price and the reliability of the potential supplier. After a brief market analysis, the candidates

have been identified and ratings for each of the two criteria have been computed $($see Table $4\mathrm{.}6).$ The supplier selection has

been conducted by using two different methods, which are variants of the weighted scoring method: the absolute weighted

scoring method $($AWSM$)$ and the relative weighted scoring method $($RWSM$).$ In AWSM, the score of a supplier is given

by considering the judgement value expressed on each criterion independently from the values given for the same

judgement to the other suppliers. In RWSM$,$ the judgement value on a criterion depends on the worst value assigned the

other suppliers for the same criterion. The company has decided to give a $40\%(a=0\mathrm{.}4)$ weight to the price criterion and a

$60\%($i$.$e$.,{?}^{1-})$ weight to the reliability. Determine the supplier to be selected by using AWSM and RWSM$.$ Discuss how

the solution changes for different values of parameter ${?}^a.$

Table $4\mathrm{.}6$ Potential suppliers and absolute judgements on the two criteria adopted by Alphen

Note: unless you code a parametrized version of these methods, it will be impossible to do by hand an

exhaustive analysis for all values of $.$ Please solve for $in\{0\mathrm{.}0,0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,0\mathrm{.}8,1\mathrm{.}0\}$ to drive your analysis.