The Smithson's family is looking for a car that satisfies three main criteria they have in mind: 1) Price, 2) safety and 3) capacity. There are three alternatives in mind while analyzing this multi- criteria decision making problem using an AHP method: Car 1, Car 2 and Car 3.

When comparing the three alternatives with regard to price, Car 1 is moderately preferred to Car 2. Car 3 is moderately preferred to Car 1, and very strongly preferred to Car 2.

With regard to safety, Car 2 is strongly preferred to Car 1, and it is moderately preferred to Car 3. Car 3 is equally to moderately preferred to Car 1.

With regard to capacity, Car 1 is moderately preferred to Car 2, and very strongly preferred to Car 3. Car 2 is equally to moderately preferred to Car 3.

The three selecting criteria have been compared with each other too: Price is equally preferred comparing to safety, and it is moderately to strongly preferred to capacity. Safety is strongly preferred to capacity.

Based on the provided data, develop you AHP model, construct all necessary matrices, conduct your calculations, and make the final conclusion on what car is the best for this family.