(3) A motorist is using the AHP to choose a new car from three possible models: an Arrow, a Bestmobile and a Commuter. The choice will be based on just two attributes, Cost and Style. The motorist considers that Cost is ‘weakly more important’ than Style.

When asked to compare the cost of the cars, the motorist makes the following statements: On cost, the Bestmobile is ‘weakly preferred’ to the Arrow, but the Arrow is ‘weakly preferred’ to the Commuter. Also, the Bestmobile is ‘extremely preferred’ to the Commuter.

On style, the Arrow is ‘very strongly preferred’ to the Bestmobile, but the Commuter is ‘weakly preferred’ to the Arrow. Also, the Commuter is ‘extremely preferred’ to the Bestmobile.

(a) Construct a hierarchy to represent the decision problem.

(b) Use an appropriate software package, or the approximation method, to calculate the weights for each table in the hierarchy and hence determine which car should be purchased.

(c) Calculate the inconsistency ratios for the motorist’s comparisons of the cars on (i) cost and (ii) style and interpret your results (use either your software or the approximation method here).