M1-4 George Lyon is about to buy a compact stereo cassette player. He is currently considering three brands—Sun, Hitek, and Surgo. The important factors to George are the price, color, warranty, size of the unit, and brand name. George has determined factor weights of 0.4, 0.1, 0.1, 0.1, and 0.3, respectively. Furthermore, George has determined factor evaluations for all of the factors for the three different manufacturers of the unit he is considering. The Sun unit has factor evaluations of 0.7, 0.9, 0.8, 0.8 and 0.9 for the price, color, warranty, size, and brand-name factors. The Hitek unit has factor evaluations of 0.6, 0.9, 0.9, 0.8, and 0.9 for these factors. Finally, Surgo has factor evaluations of 0.8, 0.4, 0.4, 0.2, and 0.6 for the same factors of price, color, warranty, size, and brand name. Determine the total weighted evaluation for the three manufacturers. Which one should George select?

M1-5 Linda Frieden is thinking about buying a new car. She is considering three different car models: car 1, car 2, and car 3. An important factor for Linda is the price. She has determined that car 1 is equally to moderately preferred to car 2. Car 1 is very strongly preferred to car 3, and car 2 is moderately to strongly preferred to car 3. Determine the priorities or factor evaluations for the three cars for price. What is the consistency ratio?

M1-6 Linda Frieden (Problem M1-5 ) is also concerned about the warranty for the three cars she is considering. The second car is moderately preferred to the first car in terms of warranty. The third car is very to extremely strongly preferred over the first car, and the third car is strongly preferred over the second car. Determine the factor evaluations or priorities for the three cars for car warranty. Compute the consistency ratio.

M1-7 Linda Frieden (Problems M1-5 and M1-6) would like to consider style as an important factor in making a decision to purchase a new car. Car 2 is moderately preferred to car 1 in terms of style, but car 1 is moderately preferred to car 3 in terms of style. Furthermore, car 2 is very to extremely strongly preferred over car 3. Determine the factor evaluations for style concerning the three cars and compute the necessary ratio.

M1-8 Linda Frieden (Problems M1-5 to M1-7) now must determine the relative weights for the three factors of price, warranty, and style. She believes that the price is equally to moderately preferred over warranty and that price is extremely preferred to style. She also believes that the car warranty is strongly to very strongly preferred over the style. Using this information, determine the weights for these three factors. Also determine the consistency ratio to make sure that the values are consistent enough to use in the analysis. In Problems M1-5 to M1-7, Linda has determined factor evaluations for price, warranty, and style for the three cars. Using the information you determined in this problem, along with the solutions to the three preceding problems, determine the final ranking for each car. Which car should be selected?

M1-9 Gina Fox is a student who will be graduating soon, and she is planning to attend graduate school to work toward an MBA. Gina has been accepted into the graduate programs at three universities. Now she must decide which one to attend. Gina has rated each one on the cost, reputation of the program, and quality of life at the university. These ratings are summarized as follows (1 is a poor rating and 10 is perfect):

Gina has decided that cost is the overriding factor. She has given cost a weight of 0.6, reputation a weight of 0.2, and quality of life a weight of 0.2. Which university should Gina select?

M1-10 Upon reevaluating the situation, Gina Fox (see Problem M1-9 ) is not comfortable with her ratings. Therefore, she has decided to compare the universities two at a time. On cost, B is strongly preferred to A; B is moderately preferred to C; and C is moderately preferred to A. On reputation, A is very strongly preferred to B; C is moderately preferred to B; and A is strongly preferred to C. On quality of life, A and B are equally preferred; A is strongly preferred to C; and B is very strongly preferred to C. On the three factors, cost is very strongly preferred to quality of life; cost is moderately preferred to reputation; and reputation is equally to moderately preferred to quality of life.

Develop the pairwise comparison matrices that would be used with the AHP. What university should Gina select?

M1-11 Jim Locke, an undergraduate student in the ESU College of Business, is trying to decide which personal computer to purchase with the money his parents gave him for Christmas. He has reduced the number of computers he has been considering to three, calling them system 1 (S1), system 2 (S2), and system 3 (S3). For each computer, he would like to consider the price, the brand name, the memory capacity, speed, flexibility, and compatibility with existing software.

To make the correct decision, he has decided to make pairwise comparisons for all the factors. For price, the first computer system is equally to moderately preferred over the second computer system and very to extremely strongly preferred over the third computer system. The second computer system is strongly preferred over the third computer system.

For brand name, the first computer system is equally preferred to the second computer system, and the first computer system is strongly to very strongly preferred over the third computer system. The second computer system is moderately to strongly preferred over the third computer system.

When it comes to memory, the second computer is equally to moderately preferred over the first computer system, and the third computer system is very strongly preferred over the first computer system. Furthermore, the third computer system is strongly to very strongly preferred over the second computer system.

For speed, the second computer system is moderately preferred to the first computer system, but the first computer system is equally to moderately preferred over the third computer system. Furthermore, the second computer system is strongly preferred over the third computer system.

For the flexibility factor, the third computer system is very to extremely strongly preferred over the first computer system, and the second computer system is equally to moderately preferred over the first computer system. The third computer system is also moderately to strongly preferred over the second computer system.

Finally, Jim has used pairwise comparisons to look at how compatible each computer system is with the existing software. Using this analysis, he has determined that the first computer system is very to extremely strongly preferred over the second computer system when it comes to compatibility. The first computer system is moderately to strongly preferred over the third computer system, and the third computer system is moderately preferred over the second computer system.

When it comes to comparing the factors, Jim has used pairwise comparisons to look at price, brand name, memory, speed, flexibility, and compatibility. Here are the results of the analysis. Price is extremely preferred to brand name, moderately to strongly preferred to memory, strongly preferred to speed, moderately preferred to flexibility, and equally to moderately preferred to existing software compatibility. In other words, price is a very important factor. The computer’s memory is equally to moderately preferred to brand name, speed is equally preferred to brand name, flexibility is moderately to strongly preferred to brand name, and existing software compatibility is strongly preferred to brand name. In looking at memory, Jim has determined that memory is equally to moderately preferred to speed. Existing software compatibility, however, is strongly to very strongly preferred to memory, and overall flexibility is equally to moderately preferred to the computer’s memory. Existing software compatibility is strongly to very strongly preferred to speed, and flexibility is moderately preferred to speed. Finally, Jim has determined that existing software compatibility is equally to moderately preferred to flexibility.

Using all of these preferences for pairwise comparisons, determine the priorities or factor evaluations, along with the appropriate consistency ratios for price, brand name, memory, speed, flexibility, and existing software compatibility for the three different computer systems. In addition, determine the overall weights for each of the factors. Which computer system should be selected?